tag:blogger.com,1999:blog-39029657492774054532024-03-13T06:36:00.438-07:00bagi-baginak sinihttp://www.blogger.com/profile/04525620916031258334noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-3902965749277405453.post-60279247145397573242010-10-14T13:28:00.000-07:002010-10-14T13:28:59.810-07:00logika informatika<!--[if !mso]> <style>
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</div><div align="center" class="MsoNormal" style="text-align: center;"><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 14pt;">Diktat Kuliah</span></b></div><div align="center" class="MsoNormal" style="text-align: center;"><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 14pt;">Oleh :</span></b></div><div align="center" class="MsoNormal" style="text-align: center;"><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 14pt;">Sukma Puspitorini, ST</span></b></div><div align="center" class="MsoNormal" style="text-align: center;"><br />
</div><div align="center" class="MsoNormal" style="text-align: center;"><b><span lang="DA" style="font-family: "Verdana","sans-serif";">PROGRAM STUDI TEKNIK INFORMATIKA STMIK NH JAMBI</span></b></div><div align="center" class="MsoNormal" style="text-align: center;"><b><span style="font-family: "Verdana","sans-serif";">TAHUN AJARAN 2007/2008</span></b></div><div align="center" class="MsoNormal" style="text-align: center;"><br />
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</div><div class="MsoNormal" style="text-align: justify;"><b><span style="font-family: "Verdana","sans-serif";">DAFTAR ISI</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
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<tr> <td colspan="3" style="padding: 0in 5.4pt; width: 426.45pt;" valign="top" width="569"> <div class="MsoNormal" style="text-align: justify;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">BAB 1 : DASAR-DASAR LOGIKA<span> </span></span></b></div></td> </tr>
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<tr> <td style="padding: 0in 5.4pt; width: 0.45in;" valign="top" width="43"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">1.2</span></div></td> <td style="padding: 0in 5.4pt; width: 351pt;" valign="top" width="468"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Logika dan Pernyataan</span></div></td> <td style="padding: 0in 5.4pt; width: 43.05pt;" valign="top" width="57"> <div class="MsoNormal" style="text-align: justify;"><br />
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<tr> <td style="padding: 0in 5.4pt; width: 0.45in;" valign="top" width="43"> <div class="MsoNormal" style="text-align: justify;"><br />
</div></td> <td style="padding: 0in 5.4pt; width: 351pt;" valign="top" width="468"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">1.2.1 Logika</span></div></td> <td style="padding: 0in 5.4pt; width: 43.05pt;" valign="top" width="57"> <div class="MsoNormal" style="text-align: justify;"><br />
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</div></td> <td style="height: 8.45pt; padding: 0in 5.4pt; width: 351pt;" valign="top" width="468"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">1.2.2 Pernyataan (Proposisi)</span></div></td> <td style="height: 8.45pt; padding: 0in 5.4pt; width: 43.05pt;" valign="top" width="57"> <div class="MsoNormal" style="text-align: justify;"><br />
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</div></td> <td style="padding: 0in 5.4pt; width: 351pt;" valign="top" width="468"> <div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">1.2.3 Penghubung Kalimat Dan Tabel Kebenaran</span></div></td> <td style="padding: 0in 5.4pt; width: 43.05pt;" valign="top" width="57"> <div class="MsoNormal" style="text-align: justify;"><br />
</div></td> </tr>
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</div></td> <td style="padding: 0in 5.4pt; width: 351pt;" valign="top" width="468"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">1.2.4 Ingkaran (Negasi) Suatu Pernyataan</span></div></td> <td style="padding: 0in 5.4pt; width: 43.05pt;" valign="top" width="57"> <div class="MsoNormal" style="text-align: justify;"><br />
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<tr> <td style="padding: 0in 5.4pt; width: 0.45in;" valign="top" width="43"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">1.3</span></div></td> <td style="padding: 0in 5.4pt; width: 351pt;" valign="top" width="468"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Tautologi dan Kontradiksi</span></div></td> <td style="padding: 0in 5.4pt; width: 43.05pt;" valign="top" width="57"> <div class="MsoNormal" style="text-align: justify;"><br />
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<tr> <td style="padding: 0in 5.4pt; width: 0.45in;" valign="top" width="43"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">1.4</span></div></td> <td style="padding: 0in 5.4pt; width: 351pt;" valign="top" width="468"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Konvers, Invers, dan Kontraposisi.</span></div></td> <td style="padding: 0in 5.4pt; width: 43.05pt;" valign="top" width="57"> <div class="MsoNormal" style="text-align: justify;"><br />
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<tr> <td style="padding: 0in 5.4pt; width: 0.45in;" valign="top" width="43"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">1.5</span></div></td> <td style="padding: 0in 5.4pt; width: 351pt;" valign="top" width="468"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Inferensi Logika</span></div></td> <td style="padding: 0in 5.4pt; width: 43.05pt;" valign="top" width="57"> <div class="MsoNormal" style="text-align: justify;"><br />
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<tr> <td style="padding: 0in 5.4pt; width: 0.45in;" valign="top" width="43"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">1.6</span></div></td> <td style="padding: 0in 5.4pt; width: 351pt;" valign="top" width="468"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Soal Latihan</span></div></td> <td style="padding: 0in 5.4pt; width: 43.05pt;" valign="top" width="57"> <div class="MsoNormal" style="text-align: justify;"><br />
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<tr> <td colspan="3" style="padding: 0in 5.4pt; width: 426.45pt;" valign="top" width="569"> <div class="MsoNormal" style="text-align: justify;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">BAB 2 : KALIMAT BERKUANTOR<span> </span></span></b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div></td> </tr>
<tr> <td style="padding: 0in 5.4pt; width: 0.45in;" valign="top" width="43"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">2.1</span></div></td> <td style="padding: 0in 5.4pt; width: 351pt;" valign="top" width="468"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Predikat dan Kalimat Berkuantor</span></div></td> <td style="padding: 0in 5.4pt; width: 43.05pt;" valign="top" width="57"> <div class="MsoNormal" style="text-align: justify;"><br />
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<tr> <td style="padding: 0in 5.4pt; width: 0.45in;" valign="top" width="43"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">2.2</span></div></td> <td style="padding: 0in 5.4pt; width: 351pt;" valign="top" width="468"> <div class="MsoNormal" style="text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Kuantor Universal dan Kuantor Eksistensial</span></div></td> <td style="padding: 0in 5.4pt; width: 43.05pt;" valign="top" width="57"> <div class="MsoNormal" style="text-align: justify;"><br />
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<tr> <td style="padding: 0in 5.4pt; width: 0.45in;" valign="top" width="43"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">2.3</span></div></td> <td style="padding: 0in 5.4pt; width: 351pt;" valign="top" width="468"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Ingkaran Kalimat Berkuantor</span></div></td> <td style="padding: 0in 5.4pt; width: 43.05pt;" valign="top" width="57"> <div class="MsoNormal" style="text-align: justify;"><br />
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<tr> <td style="padding: 0in 5.4pt; width: 0.45in;" valign="top" width="43"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">2.4</span></div></td> <td style="padding: 0in 5.4pt; width: 351pt;" valign="top" width="468"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Kalimat Berkuantor Ganda</span></div></td> <td style="padding: 0in 5.4pt; width: 43.05pt;" valign="top" width="57"> <div class="MsoNormal" style="text-align: justify;"><br />
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<tr> <td style="padding: 0in 5.4pt; width: 0.45in;" valign="top" width="43"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">2.5</span></div></td> <td style="padding: 0in 5.4pt; width: 351pt;" valign="top" width="468"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Soal Latihan</span></div></td> <td style="padding: 0in 5.4pt; width: 43.05pt;" valign="top" width="57"> <div class="MsoNormal" style="text-align: justify;"><br />
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<tr> <td colspan="3" style="padding: 0in 5.4pt; width: 426.45pt;" valign="top" width="569"> <div class="MsoNormal" style="text-align: justify;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">BAB 3 : ALJABAR BOOLE</span></b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div></td> </tr>
<tr> <td style="padding: 0in 5.4pt; width: 0.45in;" valign="top" width="43"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">3.1</span></div></td> <td style="padding: 0in 5.4pt; width: 351pt;" valign="top" width="468"> <div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Aljabar Boole Sebagai Suatu Struktur Aljabar</span></div></td> <td style="padding: 0in 5.4pt; width: 43.05pt;" valign="top" width="57"> <div class="MsoNormal" style="text-align: justify;"><br />
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<tr> <td style="padding: 0in 5.4pt; width: 0.45in;" valign="top" width="43"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">3.2</span></div></td> <td style="padding: 0in 5.4pt; width: 351pt;" valign="top" width="468"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Fungsi Boolean</span></div></td> <td style="padding: 0in 5.4pt; width: 43.05pt;" valign="top" width="57"> <div class="MsoNormal" style="text-align: justify;"><br />
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<tr> <td style="padding: 0in 5.4pt; width: 0.45in;" valign="top" width="43"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">3.3</span></div></td> <td style="padding: 0in 5.4pt; width: 351pt;" valign="top" width="468"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Ekspresi Boole</span></div></td> <td style="padding: 0in 5.4pt; width: 43.05pt;" valign="top" width="57"> <div class="MsoNormal" style="text-align: justify;"><br />
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<tr> <td style="padding: 0in 5.4pt; width: 0.45in;" valign="top" width="43"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">3.4</span></div></td> <td style="padding: 0in 5.4pt; width: 351pt;" valign="top" width="468"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Bentuk Normal Disjunctive</span></div></td> <td style="padding: 0in 5.4pt; width: 43.05pt;" valign="top" width="57"> <div class="MsoNormal" style="text-align: justify;"><br />
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<tr> <td style="padding: 0in 5.4pt; width: 0.45in;" valign="top" width="43"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">3.5</span></div></td> <td style="padding: 0in 5.4pt; width: 351pt;" valign="top" width="468"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Rangkaian Logika</span></div></td> <td style="padding: 0in 5.4pt; width: 43.05pt;" valign="top" width="57"> <div class="MsoNormal" style="text-align: justify;"><br />
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<tr> <td style="padding: 0in 5.4pt; width: 0.45in;" valign="top" width="43"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">3.6</span></div></td> <td style="padding: 0in 5.4pt; width: 351pt;" valign="top" width="468"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Soal Latihan</span></div></td> <td style="padding: 0in 5.4pt; width: 43.05pt;" valign="top" width="57"> <div class="MsoNormal" style="text-align: justify;"><br />
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<tr> <td colspan="3" style="padding: 0in 5.4pt; width: 426.45pt;" valign="top" width="569"> <div class="MsoNormal" style="text-align: justify;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">BAB 4 : METODE PEMBUKTIAN</span></b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div></td> </tr>
<tr> <td style="padding: 0in 5.4pt; width: 0.45in;" valign="top" width="43"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">4.1</span></div></td> <td style="padding: 0in 5.4pt; width: 351pt;" valign="top" width="468"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Petunjuk Umum Pembuktian</span></div></td> <td style="padding: 0in 5.4pt; width: 43.05pt;" valign="top" width="57"> <div class="MsoNormal" style="text-align: justify;"><br />
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<tr> <td style="padding: 0in 5.4pt; width: 0.45in;" valign="top" width="43"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">4.2 </span></div></td> <td style="padding: 0in 5.4pt; width: 351pt;" valign="top" width="468"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Metode Pembuktian Langsung</span></div></td> <td style="padding: 0in 5.4pt; width: 43.05pt;" valign="top" width="57"> <div class="MsoNormal" style="text-align: justify;"><br />
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<tr> <td style="padding: 0in 5.4pt; width: 0.45in;" valign="top" width="43"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">4.3</span></div></td> <td style="padding: 0in 5.4pt; width: 351pt;" valign="top" width="468"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Metode Pembuktian Tak Langsung</span></div></td> <td style="padding: 0in 5.4pt; width: 43.05pt;" valign="top" width="57"> <div class="MsoNormal" style="text-align: justify;"><br />
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</div></td> <td style="padding: 0in 5.4pt; width: 351pt;" valign="top" width="468"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">4.3.1 Pembuktian Dengan Kontradiksi</span></div></td> <td style="padding: 0in 5.4pt; width: 43.05pt;" valign="top" width="57"> <div class="MsoNormal" style="text-align: justify;"><br />
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</div></td> <td style="padding: 0in 5.4pt; width: 351pt;" valign="top" width="468"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">4.3.2 Pembuktian Dengan Kontraposisi</span></div></td> <td style="padding: 0in 5.4pt; width: 43.05pt;" valign="top" width="57"> <div class="MsoNormal" style="text-align: justify;"><br />
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<tr> <td style="padding: 0in 5.4pt; width: 0.45in;" valign="top" width="43"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">4.4 </span></div></td> <td style="padding: 0in 5.4pt; width: 351pt;" valign="top" width="468"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Soal Latihan</span></div></td> <td style="padding: 0in 5.4pt; width: 43.05pt;" valign="top" width="57"> <div class="MsoNormal" style="text-align: justify;"><br />
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</div><div align="center" class="MsoNormal" style="text-align: center;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 14pt;">PENDAHULUAN</span></b></div><div align="center" class="MsoNormal" style="text-align: center;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>Logika disebut juga <i>“the calculus of computer science”</i> karena logika memegang peranan yang sangat penting di bidang ilmu komputer. Peran kalkulus (matematika) sama pentingnya untuk ilmu-ilmu bidang sains, misalnya ilmu fisika, ilmu elektronika, ilmu kimia, dan sebagainya. Oleh karena itu, biasanya pelajar, mahasiswa, guru, dan dosen setuju bahwa logika memainkan peranan penting dalam berbagai bidang keilmuan, bahkan dalam kehidupan manusia sehari-hari.</span></div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>Logika, komputasi numerik, dan matematika diskrit memiliki peran penting dalam ilmu komputer karena semuanya berperan dalam pemrograman. Logika merupakan dasar-dasar matemtis suatu perangkat lunak, digunakan untuk memformalkan semantik bahasa pemrograman dan spesifikasi program, serta menguji ketepatan suatu program. Hal ini menunjukkan betapa pentingnya logika matematika karena banyak ilmu, khususnya dalam bidang ilmu komputer, yang memerlukan logika untuk berkembang.</span></div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>Logika dalam ilmu komputer dalam ilmu komputer digunakan sebagai dasar dalam belajar bahasa pemrograman, struktur data, kecerdasan buatan, teknik/sistem digital, basis data, teori komputasi, rekayasa perangkat lunak, sistem pakar, jaringan syaraf tiruan, dan lain-lainnya yang mempergunakan logika secara intensif. Salah satu contoh yang populer adlah sistem digital, yaitu bidang ilmu yang didasari oleh logika untuk membuat gerbang logika (<i>logic gates)</i> dan arsitektur komputer sebagai inti mikroprosesor, otak komputer atau <i><span> </span>central processing unit</i>.</span></div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>Logika matematika (<i>mathematical logic</i>) adalah cabang ilmu di bidang matematika yang memperdalam masalah logika, atau lebih tepatnya memperjelas logika dengan kaidah-kaidah matematika.</span></div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>Logika matematika sendiri juga terus berkembang, mulai dari logika proposional, logika predikat, pemrograman logika, dan sebaganya. Perkembangan terakhir ilmu logika adalah logika <i>fuzzy</i>, atau di Indonesia disebut logika kabur atau logika samar. Implementasi logika fuzzy dapat ditemui pada pengatur suhu udara (AC), mesin pencuci, kulkas, lainnya.</span></div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Dari penjelasan diatas bisa disimpulkan mengenai peran penting logika dalam ilmu komputer. <b>Jika seseorang ingin mempelajari ilmu komputer, maka ia tidak bisa terlepas dari masalah logika</b>. Oleh karena itu, <b>logika matematika</b> dipelajari secara formal di perguruan tinggi, khususnya dalam ilmu komputer sebagai <b>matakuliah wajib</b> selama 1 semester. Di indonesia sendiri ilmu komputer lebih populer dengan nama <b>Teknik Informatika</b> atau Teknologi Informasi </span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Dikutip dari buku “ Logika Matematika Untuk Ilmu Komputer”, oleh<span> </span>F. Soesianto dan Djoni Dwijono, Andi Offset, Jogjakarta.</span></div><div align="center" class="MsoNormal" style="text-align: center;"><br />
</div><div align="center" class="MsoNormal" style="text-align: center;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Jade must be carved and polished before it becomes an ornament.</span></b></div><div align="center" class="MsoNormal" style="text-align: center;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Man must be educated before he can achieve great things.</span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 16pt;"><br clear="all" style="page-break-before: always;" /> BAB 1 : DASAR-DASAR LOGIKA</span></b></div><div align="center" class="MsoNormal" style="text-align: center;"><br />
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</div><div class="MsoNormal" style="margin-left: 0.5in; text-align: justify; text-indent: -0.5in;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>1.1<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">PENGERTIAN UMUM LOGIKA</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify; text-indent: 0.5in;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Filsafat dan matematika adalah bidang pengetahuan rasional yang ada sejak dahulu. Jauh sebelum matematika berkembang seperti sekarang ini dan penerapannya menyentuh hampir seluruh bidang ilmu pengetahuan modern, ilmuwan dan filosof yunani telah mengembangkan dasar pemikiran ilmu geometri dan logika. Sebut saja THALES (640-546 SM) yaitu seorang ilmuwan geometri yang juga disebut sebagai bapak filosofi dan penalaran deduktif. Ada juga ahli matematika dan filosof PHYTAGORAS (572-497 SM) dengan dalil phytagorasnya yang terkenal yaitu a<sup>2</sup>+b<sup>2</sup>=c<sup>2</sup> .</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">MATEMATIKA DAN FILSAFAT</span></b></div><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Persamaan filsafat dan matematika</span></div><ul style="margin-top: 0in;" type="square"><li class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Kerja Filosof adalah berpikir konsep.</span></li>
<li class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Kerja Matematikawan adalah memperjelas konsep yang dikembangkan oleh filosof.</span></li>
</ul><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Perbedaan filsafat dan matematika</span></div><ul style="margin-top: 0in;" type="square"><li class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Filsafat bebas menerapkan berbagai metode rasional.</span></li>
<li class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Matematikawan hanya menerapkan metode deduksi.</span></li>
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</div><div class="MsoNormal" style="text-align: justify;"><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">MATEMATIKA DAN LOGIKA</span></b></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.5in;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Menurut BETRAND RUSSEL matematika adalah ilmu yang menyangkut deduksi logis tentang akibat-akibat dari pangkal fikir umum semua penalaran. </span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.5in;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Ini berkaitan dengan konsepsi matematika sebagai ilmu formal, ilmu tentang bilangan dan ruang, ilmu tentang besaran dan keluasan, ilmu tentang hubungan, pola bentuk, dan rakitan juga sebagai ilmu yang bersifat abstrak dan deduktif.</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">MAKNA LOGIKA</span></b></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.5in;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Berasal dari bahasa yunani “LOGOS” yang berarti kata, ucapan, atau alasan. </span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Logika adalah metode atau teknik yang diciptakan untuk meneliti ketepatan penalaran. </span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Logika mengkaji prinsip-prinsip penalaran yang benar dan penalaran kesimpulan yang absah. Ilmu ini pertama kali dikembangkan sekitar 300 SM oleh ARISTOTELES dan dikenal sebagai logika tradisioanal atau logika klasik. Dua ribu tahun kemudian dikembangkan logika modern oleh GEORGE BOOLE dan DE MORGAN yang disebut dengan Logika Simbolik karena menggunakan simbol-simbol logika secara intensif.</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.5in;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Dasar pemikiran logika klasik adalah logika benar dan salah yang disimbolkan dengan 0 (untuk logika salah) dan 1 (untuk logika benar) yang disebut juga LOGIKA BINER. Tetapi pada kenyataanya dalam kehidupan sehari-hari banyak hal yang kita jumpai yang tidak bisa dinyatakan bahwa sesuatu itu mutlak benar atau mutlak salah. Ada daerah dimana benar dan salah tersebut nilainya tidak bisa ditentukan mutlak benar atau mutlak salah alias kabur.</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.5in;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Untuk mengatasi masalah yang terjadi dalam logika klasik yang dikembangkan oleh ARISTOTELES tersebut, seorang ilmuwan dari Universitas California Berkeley, PROF. LOTFI A.ZADEH pada tahun 1965 mengenalkan suatu konsep berpikir logika yang baru yaitu LOGIKA KABUR (FUZZY LOGIC).</span></div><div class="MsoNormal" style="text-align: justify;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">PADA LOGIKA FUZZY</span></b></div><ul style="margin-top: 0in;" type="square"><li class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Nilai kebenarn bukan bersifat crisp (tegas) 0 dan 1 saja tetapi berada diantaranya (multivariabel).</span></li>
<li class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Digunakan untuk merumuskan pengetahuan dan pengalaman manusia yang mengakomodasi ketidakpastian ke dalam bentuk matematis tanpa harus mengetahui model matematikanya.</span></li>
<li class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Pada aplikasinya dalam bidang komputer, logika fuzzy diimplementasikan untuk memenuhi kebutuhan manusia akan sistem komputer yang dapat merepresentasikan cara berpikir manusia. </span></li>
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</div><div class="MsoNormal" style="text-align: justify;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">HUBUNGAN MATEMATIKA DAN LOGIKA</span></b></div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Menurut RUDOLF CARNAP (1931)</span></div><ul style="margin-top: 0in;" type="square"><li class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Konsep matematika dapat diturunkan dari konsep-konsep logika dengan melalui batasan-batasan yang jelas.</span></li>
<li class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Dalil-dalil matematika dapat diturunkan dari aksioma-aksioma logika dengan perantara deduksi logis secara murni.</span></li>
</ul><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Menurut BETRAND RUSSEL</span></div><ul style="margin-top: 0in;" type="square"><li class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Logika adalah masa muda matematika dan matematika adalah masa dewasa logika.</span></li>
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</div><div class="MsoNormal" style="text-align: justify;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">LOGIKA DAN KOMPUTER</span></b></div><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>Arsitektur sistem komputer tersusun atas rangkaian logika 1 (true) dan 0 (false) yang dikombinasikan dengan sejumlah gerbang logika AND. OR, NOT, XOR, dan NAND.</span></div><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>Program komputer berjalan di atas struktur<span> </span>penalaran yang baik dari suatu solusi terhadap suatu permasalahan dengan bantuan komponen program IF…THEN…ELSE, FOR…TO…DO, WHILE, CASE…OF.</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.5in; text-align: justify; text-indent: -0.5in;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>1.2<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">LOGIKA DAN PERNYATAAN</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.75in; text-align: justify; text-indent: -0.75in;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>1.2.1<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">LOGIKA</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">PENGERTIAN UMUM LOGIKA</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>Logika adalah metode atau teknik yang diciptakan untuk meneliti ketepatan penalaran serta mengkaji prinsip-prinsip penalaran yang benar dan penarikan kesimpulan yang absah.</span></div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>Ilmu logika berhubungan dengan kalimat-kalimat (argumen) dan hubungan yang ada diantara kalimat-kalimat tersebut. Tujuannya adalah memberikan aturan-aturan sehingga orang dapat menentukan apakah suatu kalimat bernilai benar.</span></div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>Kalimat yang dipelajari dalam logika bersifat umum, baik bahasa sehari-hari maupun bukti matematika yang didasarkan atas hipotesa-hipotesa. Oleh karena itu aturan-aturan yang berlaku di dalamnya haruslah bersifat umum dan tidak tergantung pada kalimat atau disiplin ilmu tertentu. Ilmu logika lebih mengarah dalam bentuk sintaks-sintaks daripada arti dari kalimat itu sendiri.</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">GAMBARAN UMUM LOGIKA</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>Secara umum logika dibedakan menjadi dua yaitu Logika Pasti dan Logika Tidak Pasti. Logika pasti meliputi Logika Pernyataan (Propotitional Logic), Logika Predikat (Predicate Logic), Logika Hubungan (Relation Logic) dan Logika Himpunan. Sedangkan logika tidak pasti meliputi Logika Samar atau<span> </span>kabur (Fuzzy Logic).</span></div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>Logika Pernyataan membicarakan tentang pernyataan tunggal dan kata hubungnya sehingga didapat kalimat majemuk yang berupa kalimat deklaratif. </span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.5in;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Logika Predikat<span> </span>menelaah variabel dalam suatu kalimat, kuantifikasi dan validitas sebuah argumen.</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.5in;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Logika Hubungan mempelajari hubungan antara pernyataan, relasi simetri, refleksif, antisimtris, dll.</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.5in;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Logika himpunan membicarakan tentang unsur-unsur himpunan dan hukum-hukum yang berlaku di dalamnya.</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.5in;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Logika Samar merupakan pertengahan dari dua nilai biner yaitu ya-tidak, nol-satu, benar-salah. Kondisi yang ditunjukkan oleh logika samar ini antara lain : banyak, sedikit, sekitar x, sering, umumnya.<span> </span>Logika samar banyak diterapkan dalam kecerdasan buatan, mesin pintar atau sistem cerdas dan alat-alat elektronika. Program komputer dengan menggunakan logika samar mempunyai kapasitas penyimpanan lebih kecil dan lebih cepat bila dibanding dengan logika biner.</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">ALIRAN DALAM LOGIKA</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">LOGIKA TRADISIONAL</span></div><ul style="margin-top: 0in;" type="square"><li class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Pelopornya adalah Aristoteles (384-322 SM)</span></li>
<li class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Terdiri dari analitika dan dialektika. Ilmu analitika yaitu cara penalaran yang didasarkan pada pernyataan yang benar sedangkan dialektika yaitu cara penalaran yang didasarkan pada dugaan. </span></li>
</ul><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">LOGIKA METAFISIS</span></div><ul style="margin-top: 0in;" type="square"><li class="MsoNormal" style="text-align: justify;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Dipelopori oleh F. Hegel (1770-1831 M)</span></li>
<li class="MsoNormal" style="text-align: justify;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Menurut Hegel, logika dianggap sebagai metafisika dimana susunan pikiran dianggap sebagai kenyataan.</span></li>
</ul><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">LOGIKA EPISTIMOLOGI</span></div><ul style="margin-top: 0in;" type="square"><li class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Diperkenalkan oleh FH. Bradley (1846-1924) dan Bernhard Bosanquet (1848-1923 M).</span></li>
<li class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Prisip dari logika epistimologi ini adalah untuk mencapai pengetahuan yang memadai, pikiran yang logis dan perasaan halus digabungkan. Selain itu, untuk mencapai kebenaran, logika harus dihubungkan dengan seluruh pengetahuan yang lainnya.</span></li>
</ul><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">LOGIKA INSTRUMENTALIS/FRAGMATIS</span></div><ul style="margin-top: 0in;" type="square"><li class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Dipelopori oleh Jhon Dewey (1859-1952)</span></li>
<li class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Prinsipnya adalah logika merupakan alat atau instrumen untuk menyelesaikan masalah.</span></li>
</ul><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">LOGIKA SIMBOLIS</span></div><ul style="margin-top: 0in;" type="square"><li class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Logika simbolis adalah ilmu tentang penyimpulan yang sah (absah) yang dikembangkan menggunakan metod ematematika dan bantuan simbol-simbol khusus sehingga memungkinkan seseorang menghindari makna ganda dari bahasa sehari-hari.</span></li>
</ul><ul style="margin-top: 0in;" type="square"><li class="MsoNormal" style="text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Pelopornya adalah Leibniz, De Morgan, dan Boole</span></li>
<li class="MsoNormal" style="text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Logika ini menggunakan bahasa simbol untuk mempelajari secara rinci bagaimana akal harus bekerja dan bercirikan teknis, matematis, dan ilmiah. Pemakaian simbol matematika ini untuk mewakili bahsa dalam bentuk pernyataan yang bernilai benar atau salah.</span></li>
<li class="MsoNormal" style="text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Logika simbolis ini kemudian menjadi dasar logika matematika modern yaitu logika formal yang semata-mata menelaah bentuk da bukan isi dari apa yang dibicarakan.</span></li>
</ul><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.75in; text-align: justify; text-indent: -0.75in;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>1.2.2<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">PERNYATAAN (PROPOSISI)</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify; text-indent: 0.5in;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Kata merupakan rangkaian huruf yang mengandung arti, sedangkan kalimat adalah kumpulan kata yang disusun menurut aturan tata bahasa dan mengandung arti. Di dalam matematika tidak semua pernyataan yang bernilai benar atau salah saja yang digunakan dalam penalaran. Pernyataan disebut juga kalimat deklaratif yaitu kalimat yang bersifat menerangkan. Disebut juga proposisi.</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Pernyataan/ Kalimat Deklaratif/ Proposisi adalah kalimat yang bernilai benar atau salah tetapi tidak keduanya.</span></div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Contoh :</span></div><ol start="1" style="margin-top: 0in;" type="1"><li class="MsoNormal" style="text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Yogyakarta adalah kota pelajar<span> </span>(Benar).</span></li>
<li class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">2+2=4<span> </span>(Benar).</span></li>
<li class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Semua manusia adalah fana<span> </span>(Benar).</span></li>
<li class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">4 adalah bilangan prima<span> </span>(Salah).</span></li>
<li class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">5x12=90<span> </span>(Salah).</span></li>
</ol><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Tidak semua kalimat berupa proposisi</span></div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Contoh : </span></div><ol start="1" style="margin-top: 0in;" type="1"><li class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Dimanakah letak pulau bali?.</span></li>
<li class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Pandaikah dia?.</span></li>
<li class="MsoNormal" style="text-align: justify;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Andi lebih tinggi daripada Tina.</span></li>
<li class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">3x-2y=5x+4.</span></li>
<li class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">x+y=2.</span></li>
</ol><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.75in; text-align: justify; text-indent: -0.75in;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>1.2.3<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">PENGHUBUNG KALIMAT DAN TABEL KEBENARAN</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify; text-indent: 0.5in;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Satu atau lebih proposisi dapat dikombinasikan untuk menghasilkan proposisi baru lewat penggunaan operator logika. Proposisi baru yang dihasilkan dari kombinasi tersebut disebut dengan proposisi majemuk (compound composition), sedangkan proposisi yang bukan merupakan hasil dari kombinasi proposisi lain<span> </span>disebut proposisi atomik. Proposisi majemuk tersusun dari sejumlah proposisi atomik. </span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Dalam logika dikenal 5 buah penghubung </span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: medium none; margin-left: 0.45in;"><tbody>
<tr> <td style="border: 1pt solid windowtext; padding: 0in 5.4pt;"> <div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 11pt; line-height: 150%;">Simbol</span></b></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;"> <div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 11pt; line-height: 150%;">Arti</span></b></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;"> <div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 11pt; line-height: 150%;">Bentuk</span></b></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;"> <div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span style="font-family: "Bookman Old Style","serif"; font-size: 11pt; line-height: 150%;">¬</span><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 11pt; line-height: 150%;"></span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;"> <div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 11pt; line-height: 150%;">Tidak/Not/Negasi</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;"> <div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 11pt; line-height: 150%;">Tidak………….</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;"> <div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span style="font-family: Symbol; font-size: 11pt; line-height: 150%;"><span>Ù</span></span><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 11pt; line-height: 150%;"></span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;"> <div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 11pt; line-height: 150%;">Dan/And/Konjungsi</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;"> <div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 11pt; line-height: 150%;">……..dan……..</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;"> <div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span style="font-family: Symbol; font-size: 11pt; line-height: 150%;"><span>Ú</span></span><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 11pt; line-height: 150%;"></span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;"> <div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 11pt; line-height: 150%;">Atau/Or/Disjungsi</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;"> <div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 11pt; line-height: 150%;">………atau…….</span></div></td> </tr>
<tr style="height: 23.75pt;"> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; height: 23.75pt; padding: 0in 5.4pt;"> <div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span style="font-family: Symbol; font-size: 11pt; line-height: 150%;"><span>Þ</span></span><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 11pt; line-height: 150%;"></span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 23.75pt; padding: 0in 5.4pt;"> <div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 11pt; line-height: 150%;">Implikasi</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 23.75pt; padding: 0in 5.4pt;"> <div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 11pt; line-height: 150%;">Jika…….maka…….</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;"> <div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span style="font-family: Symbol; font-size: 11pt; line-height: 150%;"><span>Û</span></span><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 11pt; line-height: 150%;"></span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;"> <div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 11pt; line-height: 150%;">Bi-Implikasi</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;"> <div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;"><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 11pt; line-height: 150%;">……..bila dan hanya bila……..</span></div></td> </tr>
</tbody></table><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 27pt; text-align: justify;"><b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 11pt;">Contoh 1.1 :</span></b></div><div class="MsoNormal" style="margin-left: 27pt; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Misalkan : p menyatakan kalimat “ Mawar adalah nama bunga”</span></div><div class="MsoNormal" style="margin-left: 27pt; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span><span> </span>Q menyatakan kalimat “ Apel adalah nama buah”</span></div><div class="MsoNormal" style="margin-left: 27pt; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Maka kalimat “ Mawar adalah nama bunga dan Apel adalah nama buah “</span></div><div class="MsoNormal" style="margin-left: 27pt; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Dinyatakan dengan simbol<span> </span><b>p </b></span><b><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> q</span></b></div><div class="MsoNormal" style="margin-left: 27pt; text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 27pt; text-align: justify;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Contoh 1.2 :</span></b></div><div class="MsoNormal" style="margin-left: 27pt; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Misalkan<span> </span>p: hari ini hari minggu</span></div><div class="MsoNormal" style="margin-left: 27pt; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span><span> </span>q: hari ini libur</span></div><div class="MsoNormal" style="margin-left: 27pt; text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">nyatakan kalimat dibawah ini dengan simbol logika :</span></div><div class="MsoNormal" style="margin-left: 45pt; text-align: justify; text-indent: -0.25in;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>a.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Hari ini tidak hari minggu tetapi libur</span></div><div class="MsoNormal" style="margin-left: 45pt; text-align: justify; text-indent: -0.25in;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>b.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Hari ini tidak hari minggu dan tidak libur</span></div><div class="MsoNormal" style="line-height: 150%; margin-left: 45pt; text-align: justify; text-indent: -0.25in;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt; line-height: 150%;"><span>c.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt; line-height: 150%;">Tidak benar bahwa hari ini hari minggu dan libur</span></div><div class="MsoNormal" style="line-height: 150%; margin-left: 27pt; text-align: justify;"><b><i><span style="font-family: "Verdana","sans-serif"; font-size: 11pt; line-height: 150%;">Penyelesaian</span></i></b></div><div class="MsoNormal" style="margin-left: 45pt; text-align: justify; text-indent: -0.25in;"><span style="font-family: "Trebuchet MS","sans-serif";"><span>a.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Kata “tetapi” mempunyai arti yang sama dengan dan sehingga kalimat (a) bisa ditulis sebagai </span><span style="font-family: "Trebuchet MS","sans-serif";">: </span><b><span style="font-family: "Bookman Old Style","serif"; font-size: 11pt;">¬</span></b><b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 11pt;">p </span></b><b><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span></b><b><span style="font-family: "Arial Unicode MS","sans-serif"; font-size: 11pt;"> q</span></b></div><div class="MsoNormal" style="margin-left: 45pt; text-align: justify; text-indent: -0.25in;"><span style="font-family: "Trebuchet MS","sans-serif";"><span>b.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><b><span style="font-family: "Bookman Old Style","serif"; font-size: 11pt;">¬</span></b><b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 11pt;">p </span></b><b><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span></b><b><span style="font-family: "Bookman Old Style","serif"; font-size: 11pt;">¬</span></b><b><span style="font-family: "Arial Unicode MS","sans-serif"; font-size: 11pt;">q</span></b></div><div class="MsoNormal" style="margin-left: 45pt; text-align: justify; text-indent: -0.25in;"><span style="font-family: "Trebuchet MS","sans-serif";"><span>c.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><b><span style="font-family: "Bookman Old Style","serif"; font-size: 11pt;">¬(</span></b><b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 11pt;">p </span></b><b><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span></b><b><span style="font-family: "Arial Unicode MS","sans-serif"; font-size: 11pt;"> q)</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">NEGASI (INGKARAN)</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Jika p adalah “ Semarang ibukota Jawa Tengah”, maka ingkaran atau negasi dari pernyataan p tersebut adalah </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p yaitu “ Semarang bukan ibukota Jawa Tengah” atau “Tidak benar bahwa Semarang ibukota Jawa Tengah”. Jika p diatas bernilai benar (true), maka ingkaran p (</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p) adalah bernilai salah (false) dan begitu juga sebaliknya.</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">KONJUNGSI</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Konjungsi adalah suatu pernyataan majemuk yang menggunakan penghubung “<b>DAN/AND</b>” dengan notasi “</span><b><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span></b><span style="font-family: "Arial Unicode MS","sans-serif"; font-size: 11pt;">”</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Contoh 1.3:</span></b></div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p: Fahmi makan nasi</span></div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Q:Fahmi minum kopi</span></div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Maka p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q : Fahmi makan nasi dan minum kopi</span></div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Pada konjungsi p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q akan bernilai benar jika baik p maupun q bernilai benar. Jika salah satunya (atau keduanya) bernilai salah maka p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q bernilai salah.</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">DISJUNGSI</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Disjungsi adalah pernyataan majemuk yang menggunakan penghubung “<b>ATAU/OR</b>” dengan notasi “</span><b><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span></b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">”.</span></div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Kalimat disjungsi dapat mempunyai 2 arti yaitu :</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>a.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">INKLUSIF OR</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Yaitu jika “p benar atau q benar atau keduanya true”</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Contoh<span> </span>: </span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: 0.25in;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p : 7 adalah bilangan prima</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: 0.25in;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q : 7 adalah bilangan ganjil</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: 0.25in;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> q : 7 adalah bilangan prima atau ganjil </span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: 0.25in;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Benar bahwa 7 bisa dikatakan bilangan prima sekaligus bilangan ganjil.</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: 0.25in;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>b.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">EKSLUSIF OR</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Yaitu jika “p benar atau q benar tetapi tidak keduanya”.</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Contoh :</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>p : Saya akan melihat pertandingan bola di TV.</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>q : Saya akan melihat pertandingan bola di lapangan.</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>p </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> q : Saya akan melihat pertandingan bola di TV atau lapangan.</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Hanya salah satu dari 2 kalimat penyusunnya yang boleh bernilai benar yaitu jika “Saya akan melihat pertandingan sepak bola di TV saja atau di lapangan saja tetapi tidak keduanya.</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">IMPLIKASI</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Misalkan ada 2 pernyataan p dan q, untuk menunjukkan atau membuktikan bahwa jika p bernilai benar akan menjadikan q bernilai benar juga, diletakkan kata “JIKA” sebelum pernyataan pertama lalu diletakkan kata “MAKA” sebelum pernyataan kedua sehingga didapatkan suatu pernyataan majemuk yang disebut dengan “IMPLIKASI/PERNYATAAN BERSYARAT/KONDISIONAL/ HYPOTHETICAL dengan notasi “</span><b><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span></b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">”.</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Notasi p</span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q dapat dibaca :</span></div><ol start="1" style="margin-top: 0in;" type="1"><li class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Jika p maka q</span></li>
<li class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q jika p</span></li>
<li class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p adalah syarat cukup untuk q</span></li>
<li class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q adalah syarat perlu untuk p</span></li>
</ol><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Contoh 1.4:</span></b></div><ol start="1" style="margin-top: 0in;" type="1"><li class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p : Pak Ali adalah seorang haji.</span></li>
</ol><div class="MsoNormal" style="margin-left: 0.5in; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q : Pak Ali adalah seorang muslim.</span></div><div class="MsoNormal" style="margin-left: 0.5in; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p </span><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> q : Jika Pak Ali adalah seorang haji maka pastilah dia seorang<span> </span>muslim.</span></div><ol start="2" style="margin-top: 0in;" type="1"><li class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p : Hari hujan.</span></li>
</ol><div class="MsoNormal" style="margin-left: 0.5in; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q : Adi membawa payung.</span></div><div class="MsoNormal" style="margin-left: 0.5in; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Benar atau salahkah pernyataan berikut?</span></div><ol start="4" style="margin-top: 0in;" type="1"><ol start="1" style="margin-top: 0in;" type="a"><li class="MsoNormal" style="text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Hari benar-benar hujan dan Adi benar-benar membawa payung.</span></li>
<li class="MsoNormal" style="text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Hari benar-benar hujan tetapi Adi tidak membawa payung.</span></li>
<li class="MsoNormal" style="text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Hari tidak hujan tetapi Adi membawa payung.</span></li>
<li class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Hari tidak hujan dan Adi tidak membawa payung.</span></li>
</ol></ol><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">BIIMPLIKASI</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Biimplikasi atau bikondosional adalah pernyataan majemuk dari dua pernyataan p dan q yang dinyatakan dengan notasi “p </span><span style="font-family: Symbol; font-size: 11pt;"><span>Û</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> q” yang bernilai sama dengan (p </span><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q) </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (q </span><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> p)<span> </span>sehingga dapat dibaca “ p jika dan hanya jika q” atau “p bila dan hanya bila q”. Biimplikasi 2 pernytaan<span> </span>hanya akan bernilai benar jika implikasi kedua kalimat penyusunnya sama-sama bernilaii benar. </span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Contoh 1.5 :</span></b></div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>p : Dua garis saling berpotongan adalah tegak lurus.</span></div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>q : Dua garis saling membentuk sudut 90 derajat.</span></div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>p </span><span style="font-family: Symbol; font-size: 11pt;"><span>Û</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> q : Dua garis saling berpotongan adalah tegak lurus jika dan hanya jika dan hanya jika dua garis saling membentuk sudut 90 derajat.</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div align="center" class="MsoNormal" style="text-align: center;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">TABEL KEBENARAN</span></b></div><div align="center" class="MsoNormal" style="text-align: center;"><br />
</div><div align="center"> <table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: medium none;"><tbody>
<tr> <td style="border: 1pt solid windowtext; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Û</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p </span><span style="font-family: Symbol; font-size: 11pt;"><span>Å</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> q</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
</tbody></table></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify; text-indent: 27pt;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Untuk menghindari perbedaan konotasi dan keganjilan arti dalam menerjemahkan simbol-simbol logika maka dalam matematika tidak disyaratkan adanya hubungan antara kedua kalimat penyusunnya. Kebenaran suatu kalimat berimplikasi semata-mata hanya tegantung pada nilai kebenaran kaliamat penyusunnya. Karena itu digunakan tabel kebenaran penghubung. Jika p dan q adalah kalimat-kalimat dimana T=true/benar dan F=false/salah, maka untuk n variable (p,q,…) maka tabel kebenaran memuat 2n baris.</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.75in; text-align: justify; text-indent: -0.75in;"><b><span style="font-family: "Verdana","sans-serif";"><span>1.2.4<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span></b><b><span style="font-family: "Verdana","sans-serif";"><span> </span>INGKARAN (NEGASI) SUATU PENYATAAN</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span style="font-family: "Verdana","sans-serif";">NEGASI SUATU KONJUNGSI</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Contoh : Fahmi makan nasi dan minum kopi</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.5in;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Suatu konjumgsi akan bernilai benar jika kedua kalimat penyusunnya yaitu p dan q bernilai benar, sedangkan negasi adalah pernyataan yang bernilai salah jika pernyataan awalnya bernilai benar<span> </span>dan bernilai benar jika pernyataan awalnya bernilai salah. </span></div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>Oleh karena itu negasi dari : “Fahmi makan nasi dan minum kopi” adalah suatu pernyataan majemuk lain yang salah satu komponennya merupakan negasi dari komponen pernyataan awalnya. Jadi negasinya adalah: “Fahmi tidak makan nasi atau tidak minum kopi”.</span></div><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Disini berlaku hukum De Morgan yaitu : </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)<span> </span>ekuivalen dengan </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span lang="DA" style="font-family: "Verdana","sans-serif";">NEGASI SUATU DISJUNGSI</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Contoh : “Fahmi makan nasi atau minum kopi”</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify; text-indent: 0.5in;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Suatu disjungsi akan bernilai salah hanya jika kedua komponen penyusunnya bernilai salah., selain itu benar. Oleh karena itu negasi dari kalimat<span> </span>diatas adalah : “ Tidak benar bahwa Fahmi makan nasi atau minum kopi” atau dapat juga dikatakan “Fahmi tidak makan nasi dan tidak minum kopi. Disini berlaku hukum De Morgan yaitu : </span><b><span style="color: red; font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span lang="DA" style="color: red; font-family: "Verdana","sans-serif"; font-size: 11pt;">(p</span></b><b><span style="color: red; font-family: Symbol; font-size: 11pt;"><span>Ú</span></span></b><b><span lang="DA" style="color: red; font-family: "Verdana","sans-serif"; font-size: 11pt;">q) </span></b><b><span style="color: red; font-family: Symbol; font-size: 11pt;"><span>º</span></span></b><b><span style="color: red; font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span></b><b><span style="color: red; font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span lang="DA" style="color: red; font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span></b><b><span style="color: red; font-family: Symbol; font-size: 11pt;"><span>Ù</span></span></b><b><span style="color: red; font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span lang="DA" style="color: red; font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">NEGASI SUATU IMPLIKASI</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Contoh</span></b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> <b>1.6</b> : “Jika hari hujan maka Adi membawa payung”.</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>Untuk memperoleh negasi dari pernyataan diatas, kita dapat mengubah bentuknya ke dalam bentuk disjungsi kemudian dinegasikan, yaitu :</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.5in;"><b><span style="color: red; font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span></b><b><span style="color: red; font-family: Symbol; font-size: 11pt;"><span>Þ</span></span></b><b><span style="color: red; font-family: "Verdana","sans-serif"; font-size: 11pt;"> q </span></b><b><span style="color: red; font-family: Symbol; font-size: 11pt;"><span>º</span></span></b><b><span style="color: red; font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span></b><b><span style="color: red; font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span style="color: red; font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span></b><b><span style="color: red; font-family: Symbol; font-size: 11pt;"><span>Ú</span></span></b><b><span style="color: red; font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></b></div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Maka negasinya</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.5in;"><b><span style="color: red; font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span style="color: red; font-family: "Verdana","sans-serif"; font-size: 11pt;">( p</span></b><b><span style="color: red; font-family: Symbol; font-size: 11pt;"><span>Þ</span></span></b><b><span style="color: red; font-family: "Verdana","sans-serif"; font-size: 11pt;"> q) </span></b><b><span style="color: red; font-family: Symbol; font-size: 11pt;"><span>º</span></span></b><b><span style="color: red; font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span></b><b><span style="color: red; font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span style="color: red; font-family: "Verdana","sans-serif"; font-size: 11pt;">(</span></b><b><span style="color: red; font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span style="color: red; font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span></b><b><span style="color: red; font-family: Symbol; font-size: 11pt;"><span>Ú</span></span></b><b><span style="color: red; font-family: "Verdana","sans-serif"; font-size: 11pt;">q) </span></b><b><span style="color: red; font-family: Symbol; font-size: 11pt;"><span>º</span></span></b><b><span style="color: red; font-family: "Verdana","sans-serif"; font-size: 11pt;"> p</span></b><b><span style="color: red; font-family: Symbol; font-size: 11pt;"><span>Ù</span></span></b><b><span style="color: red; font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span style="color: red; font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">NEGASI SUATU BIIMPLIKASI</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify; text-indent: 0.5in;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span></span></b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Biimplikasi atau bikondisional adalah pernyataan majemuk dari dua pernyataaan p dan q yang dinotasikan dengan <b>p </b></span><b><span style="font-family: Symbol; font-size: 11pt;"><span>Û</span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> q </span></b><b><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (p </span></b><b><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> q) </span></b><b><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (q </span></b><b><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> p) </span></b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">sehingga : </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(p </span><span style="font-family: Symbol; font-size: 11pt;"><span>Û</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> q) </span><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> [(p </span><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> q) </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (q </span><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> p)] </span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.5in;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span><span> </span><span> </span></span><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> [(</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q ) </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p)]</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.5in;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span><span> </span></span><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q ) </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p)</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.5in;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span></span><b><span style="color: red; font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span style="color: red; font-family: "Verdana","sans-serif"; font-size: 11pt;">(p </span></b><b><span style="color: red; font-family: Symbol; font-size: 11pt;"><span>Û</span></span></b><b><span style="color: red; font-family: "Verdana","sans-serif"; font-size: 11pt;"> q) </span></b><b><span style="color: red; font-family: Symbol; font-size: 11pt;"><span>º</span></span></b><b><span style="color: red; font-family: "Verdana","sans-serif"; font-size: 11pt;"> (p</span></b><b><span style="color: red; font-family: Symbol; font-size: 11pt;"><span>Ù</span></span></b><b><span style="color: red; font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span style="color: red; font-family: "Verdana","sans-serif"; font-size: 11pt;">q ) </span></b><b><span style="color: red; font-family: Symbol; font-size: 11pt;"><span>Ú</span></span></b><b><span style="color: red; font-family: "Verdana","sans-serif"; font-size: 11pt;"> (q</span></b><b><span style="color: red; font-family: Symbol; font-size: 11pt;"><span>Ù</span></span></b><b><span style="color: red; font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span style="color: red; font-family: "Verdana","sans-serif"; font-size: 11pt;">p)</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify; text-indent: 0.5in;"><br />
</div><div class="MsoNormal" style="margin-left: 0.5in; text-align: justify; text-indent: -0.5in;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>1.3<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">TAUTOLOGI, KONTRADIKSI, DAN CONTINGENT</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify; text-indent: 0.5in;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Tautologi adalah suatu bentuk kalimat yang selalu bernilai benar (True) tidak peduli bagaimanapun nilai kebenaran masing-masing kalimat penyusunnya, sebaliknya kontradiksi adalah suatu bentuk kalimat yang selalu bernilai salah (False), tidak peduli bagaimanapun nilai kebenaran masing-masing kalimat penyusunnya.</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.5in;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Dalam tabel kebenaran, suatu tautologi selalu bernilai True pada semua barisnya dan kontradiksi selalu bernilai False pada semua baris. Kalau suatu kalimat tautologi diturunkan lewat hukum-hukum yang ada maka pada akhirnya akan menghasilkan True, sebaliknya kontradiksi akan selalu bernilai False.</span></div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>Jika pada semua nilai kebenaran menghasilkan nilai F dan T, maka disebut <b>formula campuran (<i>contingent</i>).</b></span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Contoh 1.7 :</span></b></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>1.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Tunjukkan bahwa <b>p</b></span><b><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(</span></b><b><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p)</span></b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> adalah tautologi!</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: medium none; margin-left: 27pt;"><tbody>
<tr> <td style="border: 1pt solid windowtext; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p)</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
</tbody></table><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>2.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Tunjukkan bahwa <b>(p</b></span><b><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q) </span></b><b><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> [(</span></b><b><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p) </span></b><b><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span></b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> <b>(</b></span><b><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)]</span></b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> adalah tautologi!</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: medium none; margin-left: 27pt;"><tbody>
<tr> <td style="border: 1pt solid windowtext; padding: 0in 5.4pt;" valign="top"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q) </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> [(</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p) </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)]</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
</tbody></table><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>3.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Tunjukkan bahwa <b>(p</b></span><b><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q) </span></b><b><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> [(</span></b><b><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p) </span></b><b><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span></b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> <b>(</b></span><b><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)] </span></b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">adalah kontradiksi!</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: medium none; margin-left: 27pt;"><tbody>
<tr> <td style="border: 1pt solid windowtext; padding: 0in 5.4pt;" valign="top"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q) </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> [(</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p) </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)]</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> </tr>
</tbody></table><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">4. Tunjukkan bahwa <b>[(p</b></span><b><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q) </span></b><b><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> r] </span></b><b><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> p<span> </span></span></b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">adalah contingent!<b><span> </span></b></span></div><div class="MsoNormal" style="text-align: justify;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span></span></b></div><table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: medium none; margin-left: 27pt;"><tbody>
<tr> <td style="border: 1pt solid windowtext; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">r</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q) </span><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> r</span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">[(p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q) </span><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> r] </span><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> p<span> </span></span></div><div align="center" class="MsoNormal" style="text-align: center;"><br />
</div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> </tr>
</tbody></table><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.5in; text-align: justify; text-indent: -0.5in;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>1.4<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">KONVERS, INVERS, DAN KONTRAPOSISI</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Perhatikan pernytaan di bawah ini! </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Û</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">“Jika suatu bender adalah bendera RI maka ada warna merah pada bendera tersebut”</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Bentuk umum implikasi di atas adalah “<b>p </b></span><b><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> q</span></b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">” dengan </span></div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p : Bendera RI</span></div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q : Bendera yang ada warna merahnya.</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Dari implikasi diatas dapat dibentuk tiga implikasi lainnya yaitu :</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>1.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">KONVERS, yaitu <b>q </b></span><b><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> p</span></b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Sehingga implikasi diatas menjadi :</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">“ Jika suatu bendera ada warna merahnya, maka bendera tersebut adalah bendera RI”.</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>2.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">INVERS, yaitu </span><b><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p </span></b><b><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span></b><b><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Sehingga implikasi diatas menjadi :</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">“ Jika suatu bendera bukan bendera RI, maka pada bendera tersebut tidak ada warna merahnya”.</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>3.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">KONTRAPOSISI, yaitu </span><b><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q </span></b><b><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span></b><b><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span></b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Sehingga implikasi di atas menjadi :</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">“ Jika suatu bendera tidak ada warna merahnya, maka bendera tersebut bukan bendera RI”.</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Suatu hal yang penting dalam logika adalah kenyataan bahwa suatu implikasi selalu ekuivalen dengan kontraposisinya, akan tetapi tidak demikian halnya dengan<span> </span>invers dan konversnya.</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Hal ini dapat dilihat dari tabel kebenaran berikut</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: medium none; margin-left: 27pt;"><tbody>
<tr> <td style="border: 1pt solid windowtext; padding: 0in 5.4pt;" valign="top"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q </span><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> p</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p </span><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div class="MsoNormal" style="text-align: justify;"><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q </span><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
</tbody></table><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">INGKARAN KONVERS, INVERS, DAN KONTRAPOSISI</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Contoh 1.8: </span></b></div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Tentukan ingkaran atau negasi konvers, invers, dan kontraposisi dari implikasi berikut. </span></div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">“Jika suatu bendera adalah bendera RI maka bendera tersebut berwarna merah dan putih”</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><u><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Penyelesaian</span></u></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Misal p : Suatu bendera adalah bendera RI</span></div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>q : Bendera tersebut berwarna merah dan putih</span></div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">maka kalimatnya menjadi p </span><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> q atau jika menggunakan operator dan maka p </span><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> q ekuivalen(sebanding/</span><span style="font-family: Symbol; font-size: 11pt;"><span>»</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">) dengan<span> </span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> q. Sehingga</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>1.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Negasi dari implikasi</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Implikasi<span> </span>: (p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q) </span><span style="font-family: Symbol; font-size: 11pt;"><span>»</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> q</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Negasinya<span> </span>: </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q) </span><span style="font-family: Symbol; font-size: 11pt;"><span>»</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div><div class="MsoNormal" style="margin-left: 1.5in; text-align: justify; text-indent: -1.25in;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Kalimatnya<span> </span>:“Suatu bendera adalah bendera RI dan bendera<span> </span>tersebut tidak berwarna merah dan putih”.</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>2.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Negasi dari konvers</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Konvers <span> </span>: q</span><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p </span><span style="font-family: Symbol; font-size: 11pt;"><span>»</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Negasinya<span> </span>: </span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(</span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p) </span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>»</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> q</span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span></div><div class="MsoNormal" style="margin-left: 1.5in; text-align: justify; text-indent: -1.25in;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Kalimatnya<span> </span>: “Ada/Terdapat bendera berwarna merah dan putih tetapi bendera tersebut bukan bendera RI”.</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>3.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Negasi dari invers</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Invers<span> </span>: </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p </span><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q </span><span style="font-family: Symbol; font-size: 11pt;"><span>»</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p)</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q) </span><span style="font-family: Symbol; font-size: 11pt;"><span>»</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Negasinya<span> </span>: </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q) </span><span style="font-family: Symbol; font-size: 11pt;"><span>»</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div><div class="MsoNormal" style="margin-left: 1.5in; text-align: justify; text-indent: -1.25in;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Kalimatnya<span> </span>: “Suatu bendera bukan bendera RI atau bendera tersebut berwarna merah dan putih”.</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>4.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Negasi dari kontraposisi</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Kontraposisi<span> </span>: </span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q </span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p </span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>»</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(</span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)</span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p </span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>»</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> q</span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Negasinya<span> </span>: </span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(q</span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p) </span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>»</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span></div><div class="MsoNormal" style="margin-left: 1.5in; text-align: justify; text-indent: -1.25in;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Kalimatnya<span> </span>: “ Suatu bendera tidak berwarna merah dan putih dan bendera tersebut adalah bendera RI”.</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">1.5 EKUIVALENSI LOGIKA</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span></span></b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Pada tautologi, dan juga kontradiksi, dapat dipastikan bahwa jika dua buah ekspresi logika adalah tautologi, maka kedua buah ekspresi logika tersebut ekuivalen secara logis, demikian pula jika keduanya kontradiksi. Persoalannya ada pada <i>contingent</i>, karena memiliki semua nilai T dan F. Tetapi jika urutan T dan F atau sebaliknya pada tabel kebenaran tetap pada urutan yang sama maka tetap disebut ekuivalen secara logis. Perhatikan pernyataan berikut :</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Contoh 1.9 :</span></b></div><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">1. Dewi sangat cantik dan peramah.</span></div><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">2. Dewi peramah dan sanagt cantik.</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Kedua pernyataan di atas, tanpa dipikir panjang, akan dikatakan ekuivalen atau sama saja. Dalam bentuk ekspresi logika dapat ditulis sebagai berikut :</span></div><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">A = Dewi sangat cantik.</span></div><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">B = Dewi peramah.</span></div><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Maka ekspresi logikanya :</span></div><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">1. A </span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> B</span></div><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">2. B </span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> A</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Jika dikatakan kedua buah ekspresi logika tersebut ekuivalen secara logis maka dapat ditulis A </span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> B </span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> B </span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> A. Ekuivalensi logis dari kedua ekspresi logika tersebut dapat dibuktikan dengan tabel kebenaran sebagai berikut ini :</span></div><div align="center"> <table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: medium none;"><tbody>
<tr> <td style="border: 1pt solid windowtext; padding: 0in 5.4pt; width: 12.95pt;" valign="top" width="17"> <div class="MsoNormal" style="text-align: justify;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">A</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div class="MsoNormal" style="text-align: justify;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">B</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div class="MsoNormal" style="text-align: justify;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">A</span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">B</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div class="MsoNormal" style="text-align: justify;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">B</span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">A</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 12.95pt;" valign="top" width="17"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 12.95pt;" valign="top" width="17"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 12.95pt;" valign="top" width="17"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 12.95pt;" valign="top" width="17"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> </tr>
</tbody></table></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Pembuktian dengan tabel kebenaran diatas, walaupun setiap ekspresi logika memiliki nilai T dan F, tetapi karena memiliki urutan yang sama, maka secara logis tetap dikatakan ekuivalen. Tetapi jika urutan T dan F tidak sama, maka tidak biasa dikatakan ekuivalen secara logis. Tabel kebenaran merupakan alat untuk membuktikan kebenaran ekuivalensi secara logis. Kesimpulan diambil berdasarkan hasil dari tabel kebenaran tersebut. Lihat pernyataan berikut ini :</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Contoh 1.10 :</span></b></div><div class="MsoNormal" style="text-align: justify;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">1. Badu tidak pandai, atau dia tidak jujur.</span></div><div class="MsoNormal" style="text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">2. Adalah tidak benar jika Badu pandai dan jujur.</span></div><div class="MsoNormal" style="text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Secara intuitif dapat ditebak bahwa kedua pernyataan di atas sebenarnya sama, tetapi bagaimana jika idbuktikan dengan menggunkan tabel kebenaran berdasarkan ekspresi logika. Adapaun langkah-langkahnya :</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">1. Ubah dahulu argumen di atas ke dalam bentuk ekspresi/notasi logika.</span></div><div class="MsoNormal" style="text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>Misal : A=Badu pandai</span></div><div class="MsoNormal" style="text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span><span> </span>B=Badu jujur</span></div><div class="MsoNormal" style="text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>Maka kalimatnya menjadi</span></div><div class="MsoNormal" style="text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>1. </span><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">A</span><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">B</span></div><div class="MsoNormal" style="text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>2. </span><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(A</span><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">B)</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">2. Buat tabel kebenarannya</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div align="center"> <table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: medium none;"><tbody>
<tr> <td style="border: 1pt solid windowtext; padding: 0in 5.4pt; width: 18.35pt;" width="24"> <div align="center" class="MsoNormal" style="text-align: center;"><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">A</span></b></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;"> <div align="center" class="MsoNormal" style="text-align: center;"><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">B</span></b></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;"> <div align="center" class="MsoNormal" style="text-align: center;"><b><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">A</span></b></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;"> <div align="center" class="MsoNormal" style="text-align: center;"><b><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">B</span></b></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;"> <div align="center" class="MsoNormal" style="text-align: center;"><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">A</span></b><b><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span></b><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">B</span></b></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;"> <div align="center" class="MsoNormal" style="text-align: center;"><b><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">A</span></b><b><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span></b><b><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">B</span></b></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;"> <div align="center" class="MsoNormal" style="text-align: center;"><b><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(A</span></b><b><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span></b><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">B)</span></b></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 18.35pt;" valign="top" width="24"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 18.35pt;" valign="top" width="24"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 18.35pt;" valign="top" width="24"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 18.35pt;" valign="top" width="24"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
</tbody></table></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Perhatikan ekspresi di atas</span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">! Meskipun kedua ekspresi logika di atas memiliki nilai kebenaran yang sama, ada nilai T dan F, keduanya baru dikatakan ekuivalen secara logis jika dihubungkan dengan perangkai ekuivalensi dan akhirnya menghasilkan tautologi.</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">3. Tambahkan perangkai biimplikasi untuk menghasilkan tautologi</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div align="center"> <table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: medium none;"><tbody>
<tr> <td style="border: 1pt solid windowtext; padding: 0in 5.4pt;"> <div align="center" class="MsoNormal" style="text-align: center;"><b><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">A</span></b><b><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span></b><b><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">B</span></b></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;"> <div align="center" class="MsoNormal" style="text-align: center;"><b><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(A</span></b><b><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span></b><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">B)</span></b></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><b><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">A</span></b><b><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span></b><b><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">B </span></b><b><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Û</span></span></b><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span></b><b><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(A</span></b><b><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span></b><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">B)</span></b></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
</tbody></table></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Jika hasilnya adalah tautologi (bernilai T semua), maka dikatakan bahwa kedua argumen tersebut ekuivalen secara logis.</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">1.5.1 HUKUM-HUKUM EKUIVALENSI LOGIKA</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div align="center"> <table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: medium none; width: 523px;"><tbody>
<tr style="height: 17.5pt;"> <td style="border: 1pt solid windowtext; height: 17.5pt; padding: 0in 5.4pt; width: 95.4pt;" valign="top" width="127"> <div class="MsoNormal"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Identitas</span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; height: 17.5pt; padding: 0in 5.4pt; width: 153pt;" valign="top" width="204"> <div class="MsoNormal"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">1 </span></b><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> <span lang="ES">p<span> </span></span><span lang="ES"></span></span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; height: 17.5pt; padding: 0in 5.4pt; width: 2in;" valign="top" width="192"> <div class="MsoNormal"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">0 </span></b><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> <span lang="ES">p</span><span lang="ES"></span></span></div></td> </tr>
<tr style="height: 17.6pt;"> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; height: 17.6pt; padding: 0in 5.4pt; width: 95.4pt;" valign="top" width="127"> <div class="MsoNormal"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Ikatan</span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span></span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 17.6pt; padding: 0in 5.4pt; width: 153pt;" valign="top" width="204"> <div class="MsoNormal"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">1 </span></b><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> <b><span lang="ES">T</span></b><span lang="ES"></span></span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 17.6pt; padding: 0in 5.4pt; width: 2in;" valign="top" width="192"> <div class="MsoNormal"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">0 </span></b><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> <b><span lang="ES">0</span></b><span lang="ES"></span></span></div></td> </tr>
<tr style="height: 17.45pt;"> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; height: 17.45pt; padding: 0in 5.4pt; width: 95.4pt;" valign="top" width="127"> <div class="MsoNormal"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Idempoten</span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 17.45pt; padding: 0in 5.4pt; width: 153pt;" valign="top" width="204"> <div class="MsoNormal"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p </span><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> <span lang="ES">p</span><span lang="ES"></span></span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 17.45pt; padding: 0in 5.4pt; width: 2in;" valign="top" width="192"> <div class="MsoNormal"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p </span><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> <span lang="ES">p</span><span lang="ES"></span></span></div></td> </tr>
<tr style="height: 17.45pt;"> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; height: 17.45pt; padding: 0in 5.4pt; width: 95.4pt;" valign="top" width="127"> <div class="MsoNormal"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Negasi</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 17.45pt; padding: 0in 5.4pt; width: 153pt;" valign="top" width="204"> <div class="MsoNormal"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p </span><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> 1</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 17.45pt; padding: 0in 5.4pt; width: 2in;" valign="top" width="192"> <div class="MsoNormal"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p </span><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> 0</span></div></td> </tr>
<tr style="height: 17.2pt;"> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; height: 17.2pt; padding: 0in 5.4pt; width: 95.4pt;" valign="top" width="127"> <div class="MsoNormal"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Negasi Ganda</span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 17.2pt; padding: 0in 5.4pt; width: 153pt;" valign="top" width="204"> <div class="MsoNormal"><span style="font-family: Symbol; font-size: 11pt;"><span>Ø<span>Ø</span></span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p </span><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> <span lang="IT">p</span><span lang="IT"></span></span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 17.2pt; padding: 0in 5.4pt; width: 2in;" valign="top" width="192"> <div class="MsoNormal"><br />
</div></td> </tr>
<tr style="height: 16.9pt;"> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; height: 16.9pt; padding: 0in 5.4pt; width: 95.4pt;" valign="top" width="127"> <div class="MsoNormal"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Komutatif</span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 16.9pt; padding: 0in 5.4pt; width: 153pt;" valign="top" width="204"> <div class="MsoNormal"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q </span><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> <span>q</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p<span> </span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 16.9pt; padding: 0in 5.4pt; width: 2in;" valign="top" width="192"> <div class="MsoNormal"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q </span><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> <span>q</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div></td> </tr>
<tr style="height: 18.05pt;"> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; height: 18.05pt; padding: 0in 5.4pt; width: 95.4pt;" valign="top" width="127"> <div class="MsoNormal"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Asosiatif</span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 18.05pt; padding: 0in 5.4pt; width: 153pt;" valign="top" width="204"> <div class="MsoNormal"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(<span>p</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">)</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">r </span><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> <span>p</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(<span>q</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">r</span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">)</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 18.05pt; padding: 0in 5.4pt; width: 2in;" valign="top" width="192"> <div class="MsoNormal"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(<span>p</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">)</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">r</span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> <span>p</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(<span>q</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">r</span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">)</span></div></td> </tr>
<tr style="height: 17.15pt;"> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; height: 17.15pt; padding: 0in 5.4pt; width: 95.4pt;" valign="top" width="127"> <div class="MsoNormal"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Distributif</span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 17.15pt; padding: 0in 5.4pt; width: 153pt;" valign="top" width="204"> <div class="MsoNormal"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(<span>q</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">r</span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">) </span><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (<span>p</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">)</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(<span>p</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">r</span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">)</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 17.15pt; padding: 0in 5.4pt; width: 2in;" valign="top" width="192"> <div class="MsoNormal"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(<span>q</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">r</span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">) </span><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (<span>p</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">)</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(<span>p</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">r</span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">)</span></div></td> </tr>
<tr style="height: 18.35pt;"> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; height: 18.35pt; padding: 0in 5.4pt; width: 95.4pt;" valign="top" width="127"> <div class="MsoNormal"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">De Morgan’s</span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 18.35pt; padding: 0in 5.4pt; width: 153pt;" valign="top" width="204"> <div class="MsoNormal"><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(<span>p</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">) </span><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 18.35pt; padding: 0in 5.4pt; width: 2in;" valign="top" width="192"> <div class="MsoNormal"><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(<span>p</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">) </span><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div></td> </tr>
<tr style="height: 18.35pt;"> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; height: 18.35pt; padding: 0in 5.4pt; width: 95.4pt;" valign="top" width="127"> <div class="MsoNormal"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Aborbsi</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 18.35pt; padding: 0in 5.4pt; width: 153pt;" valign="top" width="204"> <div class="MsoNormal"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q) </span><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> p</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; height: 18.35pt; padding: 0in 5.4pt; width: 2in;" valign="top" width="192"> <div class="MsoNormal"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q) </span><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> p</span></div></td> </tr>
</tbody></table></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Selain dengan menggunkan tabel kebenaran, menentukan dua buah argumen adalah ekuivalen secara logis dapat juga menggunakan hukum-hukum ekuivalensi logika. Cara ini lebih singkat </span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Contoh 1.11 :</span></b></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>1.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Buktikan ekuivalensi kalimat di bawah ini dengan hukum-hukum ekuivalensi.</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(<span>p</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q) </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q) </span><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><u><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Penyelesaian</span></u></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(<span>p</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q) </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q) </span><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> <span lang="DA">(</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)) </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span><span> </span></span><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q) </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span><span> </span></span><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (<span>q</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)</span></div><div class="MsoNormal" style="margin-left: 0.5in; text-align: justify; text-indent: -0.25in;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span><span> </span></span><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> T</span></div><div class="MsoNormal" style="margin-left: 0.5in; text-align: justify; text-indent: -0.25in;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span><span> </span></span><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p <span> </span>Terbukti</span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Dalam membuktikan ekuivalensi p</span><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q ada 3 macam cara yang bisa dilakukan :</span></div><ol start="1" style="margin-top: 0in;" type="1"><li class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">P diturunkan terus menerus (dengan menggunakan hukum-hukum ekuivalensi logika yang ada).</span></li>
<li class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Q diturunkan terus-menerus (dengan menggunakan hukum-hukum ekuivalensi logika yang ada), sehingga didapat P.</span></li>
<li class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">P dan Q diturunkan secara terpisah sehingga akhirnya didapat R</span></li>
</ol><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Sebagai aturan kasar, biasanya bentuk yang lebih kompleks yang diturunkan ke dalam bentuk yang sederhana. Jadi jika p kompleks amaka aturan (1) yang dilakukan. Sebaliknya jika q yang lebih kompleks maka aturan (2) yang dilakukan. Aturan (3) digunakan jika p dan q sama-sama kompleks.</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">PENYEDERHANAAN LOGIKA</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Operasi penyederhanaan menggunakan hukum-hukum ekuivalensi logis. Selanjutnya perhatikan operasi penyederhanaan berikut dengan hukum yang digunakan tertulis di sisi kanannya. Penyederhanaan ekspresi logika atau bentuk-bentuk logika ini dibuat sesederhana mungkin dan sudah tidak dimungkinkan dimanipulasi lagi.</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Contoh 1.12 :</span></b></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>1.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(p </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(</span><b><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p </span></b><b><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span></b><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span></b><b><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">)<span> </span>ingat p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><b><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(</span></b><b><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span></b><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p)</span></b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)<span> </span>ingat p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> p </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (p </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> q)<span> </span>Hk. Negasi ganda dan De Morgan</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p) </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (p</span><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)<span> </span>Hk. Distributif</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)<span> </span>Hk. Idempoten p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p </span><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> p</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> p<span> </span>Hk. Absorbsi</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>2.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (<b>p</b></span><b><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span></b><b><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">1</span></b><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">) </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)<span> </span>Hk.Identitas</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(1</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)<span> </span><span> </span>Hk.Distributif</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">1<span> </span><span> </span>Hk.Identitas </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> p<span> </span><span> </span>Hk.Identitas </span><span lang="IT" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>3.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q) </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (q</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p)</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q) </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p)<span> </span>ingat p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q) </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)<span> </span>Hk. Komutatif</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> [(</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)<span> </span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p] </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> [(</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q]<span> </span>Hk. Distributif</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> [(p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p)</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)] </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> [(</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(q</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)]<span> </span>Hk. Distributif</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> [0</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)] </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> [(</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">0]<span> </span>Hk. Kontradiksi</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)<span> </span>Hk. Identitas</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Operasi penyederhanaan dengan menggunakan hukum-hukum logika dapat digunakan untuk membuktikan suatu ekspresi logika Tautologi, Kontradiksi, maupun Contingent. Jika hasil akhir penyederhanaan ekspresi logika adalah <b>1</b>, maka ekspresi logika tersebut adalah <b>tautologi</b>. Jika hasil yang diperoleh adalah <b>0</b>, berarti ekspresi logika tersebut <b>kontradiksi</b>. Jika hasilnya <b>tidak 0 ataupun 1</b>, maka ekspresi logikanya adalah <b>contingent</b>. </span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Contoh 1.13 :</span></b></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>1.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">[(p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p]</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.25in;"><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> [(</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p] </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> q<span> </span>ingat p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.25in;"><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">[(</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p] </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> q<span> </span>ingat p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.25in;"><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> [(p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p] </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> q<span> </span>Hk. Negasi ganda dan De Morgan</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.25in;"><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> [(p</span><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p)</span><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(</span><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p)] </span><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> q<span> </span>Hk. Distributif</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.25in;"><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> [1</span><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(</span><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)] </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> q<span> </span>Hk. Idempoten dan komutatif</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.25in;"><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q<span> </span>Hk. Identitas</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.25in;"><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)<span> </span>Hk. Assosiatif</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.25in;"><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">1<span> </span>Hk. Idempoten</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.25in;"><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> 1<span> </span>Hk. Identitas</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.25in;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Karena hasil akhirnya 1, maka ekspresi logika diatas adalah tautologi.</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>2.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q) </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> [(</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p) </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)]</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.25in;"><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)<span> </span></span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.25in;"><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> [(p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p]</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">[(p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q]<span> </span>Hk. Distributif</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.25in;"><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> [(p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p)</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(q</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p)]</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">[(p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(q</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)]<span> </span>Hk. Distributif</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.25in;"><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> [0</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(q</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p)]</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">[(p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">0]<span> </span>Hk. Negasi</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.25in;"><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)<span> </span>Hk. Idempoten</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.25in;"><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p)</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(q</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)<span> </span>Hk. Assosiatif</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.25in;"><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> 0</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">0<span> </span>Hk. Negasi</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.25in;"><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> 0<span> </span>Hk. Idempoten</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.25in;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Hasil akhir 0, maka ekspresi logika diatas adalah kontradiksi.</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.25in;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>3.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">[(p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p] </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.25in;"><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> [(p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p)</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(q</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p)] </span><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q<span> </span>Hk. Distributif</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.25in;"><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> [0 </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (q</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p)] </span><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q<span> </span>Hk. Negasi</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.25in;"><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (q</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p) </span><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q<span> </span>Hk. Identitas</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.25in;"><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(q</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p) </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q<span> </span>ingat p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q </span><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.25in;"><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p) </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q<span> </span>Hk. De Morgan</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.25in;"><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> (</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p<span> </span>Hk. Assosiatif</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.25in;"><span style="font-family: Symbol; font-size: 11pt;"><span>º</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span><span style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p<span> </span>Hk. Idempoten</span></div><div class="MsoNormal" style="text-align: justify; text-indent: 0.25in;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Hasilnya bukan 0 atau 1,<span> </span>ekspresi logika di atas adalah contingent.</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span></span></div><div class="MsoNormal" style="margin-left: 0.5in; text-align: justify; text-indent: -0.5in;"><b><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>1.5<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span></b><b><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">INFERENSI LOGIKA</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.75in; text-align: justify; text-indent: -0.75in;"><b><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>1.5.1<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span></b><b><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">ARGUMEN VALID DAN INVALID</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Argumen </span></b><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">adalah suatu pernyataan tegas yang diberikan oleh sekumpulan proposisi P<sub>1</sub>,<span> </span>P<sub>2</sub>, .........,P<sub>n</sub> yang disebut <b>premis</b> (hipotesa/asumsi) dan menghasilkan proposisi Q yang lain yang disebut <b>konklusi </b>(kesimpulan).</span></div><div class="MsoNormal" style="text-align: justify;"><span style="height: 98px; left: 0px; margin-left: 407px; margin-top: 2px; position: absolute; width: 14px; z-index: 251659776;"><img height="98" src="file:///C:/DOCUME%7E1/glow/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image003.gif" width="14" /></span><span style="height: 136px; left: 0px; margin-left: 372px; margin-top: 3px; position: absolute; width: 52px; z-index: 251654656;"><img height="136" src="file:///C:/DOCUME%7E1/glow/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image004.gif" width="52" /></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Secara umum di notasikan dengan </span></div><div class="MsoNormal" style="text-align: justify;"><span> <table align="left" cellpadding="0" cellspacing="0"><tbody>
<tr> <td height="3" width="407"><br />
</td> </tr>
<tr> <td><br />
</td> <td><img height="99" src="file:///C:/DOCUME%7E1/glow/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image005.gif" width="87" /></td> </tr>
</tbody></table></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span></div><br clear="ALL" /> <div class="MsoNormal" style="text-align: justify;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>P<sub>1,</sub>P<sub>2, ..........,</sub>P<sub>n</sub> </span><span lang="IT" style="font-family: "Arial","sans-serif"; font-size: 11pt;">├Q<span> </span>atau dapat juga ditulis </span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div><div class="MsoNormal" style="text-align: justify;"><span> <table align="left" cellpadding="0" cellspacing="0"><tbody>
<tr> <td height="3" width="59"><br />
</td> <td width="74"><br />
</td> <td width="2"><br />
</td> <td width="20"><br />
</td> <td width="26"><br />
</td> <td width="18"><br />
</td> </tr>
<tr> <td height="1"><br />
</td> <td align="left" rowspan="5" valign="top"><img height="47" src="file:///C:/DOCUME%7E1/glow/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image006.gif" width="74" /></td> </tr>
<tr> <td height="14"><br />
</td> <td colspan="2"><br />
</td> <td align="left" valign="top"><img height="14" src="file:///C:/DOCUME%7E1/glow/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image007.gif" width="26" /></td> </tr>
<tr> <td height="3"><br />
</td> </tr>
<tr> <td height="22"><br />
</td> <td><br />
</td> <td bgcolor="white" colspan="3" height="22" style="-moz-background-clip: border; -moz-background-inline-policy: continuous; -moz-background-origin: padding; background: white none repeat scroll 0% 0%; vertical-align: top;" width="64"><span style="left: 0pt; position: absolute; z-index: 251658752;"> <table cellpadding="0" cellspacing="0"><tbody>
<tr> <td> <div class="shape" style="padding: 0pt;"> <div class="MsoNormal">Konklusi</div></div></td> </tr>
</tbody></table></span> </td> </tr>
<tr> <td height="7"><br />
</td> </tr>
</tbody></table></span><b><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><br />
</div><br clear="ALL" /> <div class="MsoNormal" style="text-align: justify;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Nilai kebenaran suatu argumen ditentukan sebagai berikut :</span></div><div class="MsoNormal" style="text-align: justify;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">“ <i>Suatu argumen P<sub>1,</sub>P<sub>2,…………,,</sub>P<sub>n</sub> </i></span><b><span lang="IT" style="font-size: 11pt;">├</span></b><i><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> Q dikatakan benar</span></i><b><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span></b><i><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(valid) jika Q bernilai benar untuk semua premis yang benar dan argumen dalam keadaan selain itu dikatakan salah (invalid/fallacy)”.</span></i></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Dengan kata lain, suatu argumen dikatakan valid apabila untuk sembarang pernyataan yang disubtitusikan ke dalam premis, jika semua premis benar maka konklusinya juga benar. Sebaliknya jika semua premis benar tetapi konklusinya ada yang salah maka argumen tersebut dikatakan <i>invalid</i> (fallacy).</span></div><div class="MsoNormal" style="text-align: justify;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Jadi suatu argumen dikatakan <i>valid </i><span> </span><b>jika dan hanya jika </b>proposisi P<sub>1</sub></span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">P<sub>2</sub></span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">........</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">P<sub>n</sub>) </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> Q adalah sebuah <b>Tautolog</b>i.</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Contoh 1.14 :</span></b><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>1.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Premis </span></div><div class="MsoNormal" style="margin-left: 0.5in; text-align: justify;"><span lang="IT" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">P<sub>1</sub> : Jika Office dan Delphi diperlukan maka semua orang akan<span> </span>belajar<span> </span>komputer</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: 0.25in;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">P<sub>2</sub> : Office dan Delphi diperlukan</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Konklusi </span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>Q : Semua orang akan belajar komputer</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Jika ditulis dalam bentuk notasi logika</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Misal p : Office dan Delphi diperlukan</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>q : Semua orang belajar komputer</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Maka argumen diatas dapat ditulis :</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q, p </span><span lang="DA" style="font-family: "Arial","sans-serif"; font-size: 11pt;">├ </span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q<span> </span>(valid)</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>2.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Misal p : Saya suka kalkulus</span></div><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>q : Saya lulus ujian kalkulus</span></div><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>Maka argumen p </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> q, p </span><span lang="DA" style="font-family: "Arial","sans-serif"; font-size: 11pt;">├ </span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q dapat ditulis</span></div><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>P<sub>1</sub> : Jika saya suka kalkulus, maka saya akan lulus ujian kalkulus</span></div><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span>P<sub>2</sub> : Saya lulus ujian kalkulus</span></div><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span></span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>\</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> Saya lulus ujian kalkulus (valid)</span></div><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Untuk mengetahui suatu argumen apakah valid atau tidak maka dapat dilakukan langkah-langkah sebagai berikut :</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>1.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Tentukan premis dan konklusi argumen</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>2.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Buat tabel yang menunjukkan nilai kebenaran untuk semua premis dan konklusi.</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>3.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Carilah baris kritis yatitu baris diman semua premis bernilai benar.</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>4.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Dalam baris kritis tersebut, jika nilai kesimpulan semuanya benar maka argumen tersebut valid. Jika diantara baris kritis tersebut ada baris dengan nilai konklusi salah maka argumen tersebut tidak valid.</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Contoh 1.15:</span></b></div><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Tentukan apakah argumen berikut ini valid atau invalid</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>a)<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(q</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">r), </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">r </span><span lang="DA" style="font-family: "Arial","sans-serif"; font-size: 11pt;">├ </span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>b)<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(q</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">r), q</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">r) </span><span lang="DA" style="font-family: "Arial","sans-serif"; font-size: 11pt;">├</span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">r</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Penyelesaian </span></div><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">a) </span></div><table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: medium none; margin-left: 5.4pt;"><tbody>
<tr> <td style="border: 1pt solid windowtext; padding: 0in 5.4pt; width: 49.95pt;" valign="top" width="67"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Baris ke</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">r</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">r</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(q</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">r)<br />
(Premis)</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">r</span></div><div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(Premis)</span></div></td> <td style="border-color: windowtext windowtext windowtext -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div><div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(konklusi)</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 49.95pt;" valign="top" width="67"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">1</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 49.95pt;" valign="top" width="67"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">2</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="-moz-background-clip: border; -moz-background-inline-policy: continuous; -moz-background-origin: padding; background: rgb(204, 204, 204) none repeat scroll 0% 0%; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="-moz-background-clip: border; -moz-background-inline-policy: continuous; -moz-background-origin: padding; background: rgb(204, 204, 204) none repeat scroll 0% 0%; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="-moz-background-clip: border; -moz-background-inline-policy: continuous; -moz-background-origin: padding; background: rgb(204, 204, 204) none repeat scroll 0% 0%; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 49.95pt;" valign="top" width="67"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">3</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 49.95pt;" valign="top" width="67"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">4</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="-moz-background-clip: border; -moz-background-inline-policy: continuous; -moz-background-origin: padding; background: rgb(204, 204, 204) none repeat scroll 0% 0%; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="-moz-background-clip: border; -moz-background-inline-policy: continuous; -moz-background-origin: padding; background: rgb(204, 204, 204) none repeat scroll 0% 0%; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="-moz-background-clip: border; -moz-background-inline-policy: continuous; -moz-background-origin: padding; background: rgb(204, 204, 204) none repeat scroll 0% 0%; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 49.95pt;" valign="top" width="67"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">5</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 49.95pt;" valign="top" width="67"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">6</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="-moz-background-clip: border; -moz-background-inline-policy: continuous; -moz-background-origin: padding; background: rgb(204, 204, 204) none repeat scroll 0% 0%; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="-moz-background-clip: border; -moz-background-inline-policy: continuous; -moz-background-origin: padding; background: rgb(204, 204, 204) none repeat scroll 0% 0%; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="-moz-background-clip: border; -moz-background-inline-policy: continuous; -moz-background-origin: padding; background: rgb(204, 204, 204) none repeat scroll 0% 0%; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 49.95pt;" valign="top" width="67"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">7</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> </tr>
<tr> <td style="border-color: -moz-use-text-color windowtext windowtext; border-style: none solid solid; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 49.95pt;" valign="top" width="67"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">8</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">T</span></div></td> <td style="border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-style: none solid solid none; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt;" valign="top"> <div align="center" class="MsoNormal" style="text-align: center;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">F</span></div></td> </tr>
</tbody></table><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Dapat dilihat pada tabel diatas bahwa baris 2, 4, dan 6 premisnya bernilai benar semua. Kemudian lihat pada baris konklusi. </span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Ternyata pada baris konklusi semuanya bernilai benar. Maka argumen diatas adalah valid.</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">b) Silahkan Anda kerjakan!.</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.75in; text-align: justify; text-indent: -0.75in;"><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>1.5.2<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span></b><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">ATURAN PENARIKAN KESIMPULAN</span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>A.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">MODUS PONEN</span></b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Modus ponen atau penalaran langsung adalh salah satu metode inferensi dimana jika diketahui implikasi ” Bila p maka q ” yang diasumsikan bernilai benar dan antasenden (p) benar. Supaya implikasi p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q bernilai benar, maka q juga harus bernilai benar.</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Modus Ponen : p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q , p </span><span lang="DA" style="font-family: "Arial","sans-serif"; font-size: 11pt;">├ </span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q </span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">atau dapat juga ditulis<span> </span></span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Arial","sans-serif"; font-size: 11pt;">――――</span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>\</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> q</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Contoh 1.16 :</span></b></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Jika digit terakhir suatu bilangan adalah 0, maka bilangan tersebut habis dibagi 10</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Digit terakhir suatu bilangan adalah 0</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Arial","sans-serif"; font-size: 11pt;">――――――――――――――――――――――――――――――――――――</span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>\</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> Bilangan tersebut habis dibagi 10</span></div><div class="MsoNormal" style="text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span> </span></span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>B.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span></b><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">MODUS TOLLENS</span></b></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Bentuk modus tollens mirip dengan modus ponen, hanya saja premis kedua dan kesimpulan merupakan kontraposisi premis pertama modus ponen. Hal ini mengingatkan bahwa suatu implikasi selalu ekuivalen dengan kontraposisinya. </span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Modus Tollens : p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q, </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q </span><span lang="DA" style="font-family: "Arial","sans-serif"; font-size: 11pt;">├ </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Atau dapat juga ditulis</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Arial","sans-serif"; font-size: 11pt;">――――</span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>\</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> </span><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Contoh 1.17:</span></b></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Jika digit terakhir suatu bilangan adalah 0, maka bilangan tersebut habis dibagi 10</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Suatu bilangan tidak habis dibagi 10</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Arial","sans-serif"; font-size: 11pt;">――――――――――――――――――――――――――――――――――――</span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>\</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> Digit terakhir bilangan tersebut bukan 0</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>C.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span></b><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">PENAMBAHAN DISJUNGTIF (ADDITION)</span></b></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Inferensi penambahan disjungtif didasarkan atas fakta bahwa suatu kalimat dapat digeneralisasikan dengan penghubung ”</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">”. Alasannya adalah karena penghubung ”</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">” bernilai benar jika salah satu komponennya bernilai benar. </span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Misalnya saya mengatakan ”Langit berwarna biru” (bernilai benar). Kalimat tersebut tetap akan bernilai benar jika ditambahkan kalimat lain dengan penghubung ”</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">”. Misalnya ”Langit berwarna biru atau bebek adalah binatang menyusui”. Kalimat tersebut tetap bernilai benar meskipun kalimat ”Bebek adalah binatang menyusui”, merupakan kalimat yang bernilai salah.</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Addition : p </span><span style="font-family: "Arial","sans-serif"; font-size: 11pt;">├</span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q) atau q </span><span style="font-family: "Arial","sans-serif"; font-size: 11pt;">├ </span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">(p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q)</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Atau dapat ditulis</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p<span> </span><span> </span>atau <span> </span>q</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Arial","sans-serif"; font-size: 11pt;">――――<span> </span>――――</span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>\</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q<span> </span></span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>\</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Contoh 1.18 :</span></b></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Simon adalah siswa SMU</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Arial","sans-serif"; font-size: 11pt;">――――――――――――――――――――</span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>\</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> Simon adalah siswa SMU atau SMP</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>D.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span></b><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">PENYEDERHAAN KONJUNGTIF (SIMPLIFICATION)</span></b></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Inferensi ini merupakan kebalikan dari inferensi penambahan disjungtif. Jika beberapa kalimat dihubungkan<span> </span>dengan operator ”</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">”, maka kalimat tersebut dapat diambil salah satunya secara khusus (penyempitan kalimat). </span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Simplification : (p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q) </span><span lang="DA" style="font-family: "Arial","sans-serif"; font-size: 11pt;">├</span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p atau (p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q) </span><span lang="DA" style="font-family: "Arial","sans-serif"; font-size: 11pt;">├ </span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Atau dapat ditulis</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q<span> </span>atau<span> </span>p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Arial","sans-serif"; font-size: 11pt;">―――<span> </span>―――</span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>\</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> p<span> </span></span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>\</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> q</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Contoh 1.19 :</span></b></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Langit berwarna biru dan bulan berbentuk bulat</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Arial","sans-serif"; font-size: 11pt;">―――――――――――――――――――――――――</span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>\</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> Langit berwarna biru atau </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>\</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> Bulan berbentuk bulat</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>E.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span></b><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">SILOGISME DISJUNGTIF</span></b></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Prinsip dasar Silogisme Disjungtif (Disjunctive syllogism) adalah kenyataan bahwa apabila kita dihadapkan pada satu diantara dua pilihan yang ditawarkan (A atau B). Sedangkan kita tidak memilih/tidak menyukai A, maka satu-satunua pilihan adalah memilih B. Begitu juga sebaliknya.</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Silogisme Disjungtif : p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q, </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p </span><span lang="DA" style="font-family: "Arial","sans-serif"; font-size: 11pt;">├</span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q dan p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q, </span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q </span><span lang="DA" style="font-family: "Arial","sans-serif"; font-size: 11pt;">├ </span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Atau dapat ditulis</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q<span> </span>atau<span> </span>p</span><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p<span> </span></span><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Ø</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Arial","sans-serif"; font-size: 11pt;">――――<span> </span>――――</span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>\</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> q<span> </span></span><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>\</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> p</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Contoh 1.20:</span></b></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Saya pergi ke mars atau ke bulan</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Saya tidak pergi ke mars</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Arial","sans-serif"; font-size: 11pt;">――――――――――――――――――</span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>\</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> Saya pergi ke bulan</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>F.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span></b><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">SILOGISME HIPOTESIS (TRANSITIVITY)</span></b></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Prinsip silogisme hipotesis adalah sifat transitif pada implikasi. Jika implikasi p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q dan q</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">r keduanya bernilai benar, maka implikasi p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">r bernilai benar pula.</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Transitivity : p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q , q</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">r </span><span style="font-family: "Arial","sans-serif"; font-size: 11pt;">├ </span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">r</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Atau dapat ditulis</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">r</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Arial","sans-serif"; font-size: 11pt;">―――――</span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>\</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> p</span><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">r</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><b><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Contoh 1.21:</span></b></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Jika hari hujan maka tanahnya menjadi berlumpur</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Jika tanahnya berlumpur maka sepatu saya akan kotor</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Arial","sans-serif"; font-size: 11pt;">―――――――――――――――――――――――――――――</span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="ES" style="font-family: Symbol; font-size: 11pt;"><span>\</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> Jika hari hujan maka sepatu saya akan kotor.</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>G.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">KONJUNGSI</span></b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Jika ada dua kalimat yang masing-masing benar, maka gabungan kedua kalimat tersebut dengan menggunakan penghubung ”</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">” juga bernilai benar.</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Konjungsi </span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Arial","sans-serif"; font-size: 11pt;">――</span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>\</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"> p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ù</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;"><span>H.<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span></b><b><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">DILEMA</span></b></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Kadang-kadang, dalam kalimat yang dihubungkan dengan penghubung ”</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">”, masing-masing kalimat dapat mengimplikasikan<span> </span>sesuatu yang sama. Berdasarkan hal itu maka suatu kesimpulan dapat diambil.</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">Dilema : </span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Ú</span></span><span lang="DA" style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">p</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">r</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">q</span><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>Þ</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">r</span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-family: "Arial","sans-serif"; font-size: 11pt;">―――</span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;"></span></div><div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span lang="DA" style="font-family: Symbol; font-size: 11pt;"><span>\</span></span><span style="font-family: "Verdana","sans-serif"; font-size: 11pt;">r</span></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="margin-left: 0.5in;"><br />
</div><div class="MsoNormal" style="margin-left: 0.5in;"><br />
</div><div class="MsoNormal"><br />
</div></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac>nak sinihttp://www.blogger.com/profile/04525620916031258334noreply@blogger.com0