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TAUTOLOGI, KONTRADIKSI, DAN CONTINGENT
PERTEMUAN KE-6 OLEH: SRI WEDA MAHENDRA,ST.
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TAUTOLOGI Tautologi adalah suatu bentuk kalimat yang selalu bernilai benar (True) tidak peduli bagaimanapun nilai kebenaran masing-masing kalimat penyusunnya KONTRADIKSI Kontradiksi adalah suatu bentuk kali-mat yang selalu bernilai salah (False), tidak peduli bagaimanapun nilai kebe-naran masing-masing kalimat penyu-sunnya.
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KONTIGENSI Kotigensi adalah suatu bentuk kalimat yang bernilai benar (True) dan salah (False) tidak peduli bagaimana pun nilai kebenaran masing-masing kalimat penyu-sunnya. Contoh: Tunjukkan apakah pernyataan berikut ini tautologi, kontradiksi atau kotigensi. 1. (pq) [(p) (q)] 2. (pq) [(p) (q)] 3. [(pq) r] p
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(pq) [(p) (q)] p q p q (pq) (pq) (pq)(p q) B B B S
![(pq) [(p) (q)] p q p q (pq) (pq) (pq)(p q) B B B S](http://slideplayer.info/slide/2898865/10/images/4/%28p%EF%83%9Aq%29+%EF%83%9A+%5B%28%EF%83%98p%29+%EF%83%99+%28%EF%83%98q%29%5D+p+q+%EF%81%BEp+%EF%81%BEq+%28p%EF%83%9Aq%29+%28%EF%81%BEp%EF%83%99%EF%81%BEq%29+%28p%EF%83%9Aq%29%EF%83%9A%28%EF%81%BEp+%EF%83%99+%EF%81%BEq%29+B+B+B+S.jpg "(pq) [(p) (q)] p q p q (pq) (pq) (pq)(p q) B B B S")
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(pq) [(p) (q)] p q p q (pq) (pq) (pq)(p q) B B S B
![(pq) [(p) (q)] p q p q (pq) (pq) (pq)(p q) B B S B](http://slideplayer.info/slide/2898865/10/images/5/%28p%EF%83%9Aq%29+%EF%83%9A+%5B%28%EF%83%98p%29+%EF%83%99+%28%EF%83%98q%29%5D+p+q+%EF%81%BEp+%EF%81%BEq+%28p%EF%83%9Aq%29+%28%EF%81%BEp%EF%83%99%EF%81%BEq%29+%28p%EF%83%9Aq%29%EF%83%9A%28%EF%81%BEp+%EF%83%99+%EF%81%BEq%29+B+B+S+B.jpg "(pq) [(p) (q)] p q p q (pq) (pq) (pq)(p q) B B S B")
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(pq) [(p) (q)] p q p q (pq) (pq) (pq)(p q) B B S S
![(pq) [(p) (q)] p q p q (pq) (pq) (pq)(p q) B B S S](http://slideplayer.info/slide/2898865/10/images/6/%28p%EF%83%9Aq%29+%EF%83%9A+%5B%28%EF%83%98p%29+%EF%83%99+%28%EF%83%98q%29%5D+p+q+%EF%81%BEp+%EF%81%BEq+%28p%EF%83%9Aq%29+%28%EF%81%BEp%EF%83%99%EF%81%BEq%29+%28p%EF%83%9Aq%29%EF%83%9A%28%EF%81%BEp+%EF%83%99+%EF%81%BEq%29+B+B+S+S.jpg "(pq) [(p) (q)] p q p q (pq) (pq) (pq)(p q) B B S S")
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(pq) [(p) (q)] p q p q (pq) (pq) (pq)(p q) B B S S
![(pq) [(p) (q)] p q p q (pq) (pq) (pq)(p q) B B S S](http://slideplayer.info/slide/2898865/10/images/7/%28p%EF%83%9Aq%29+%EF%83%9A+%5B%28%EF%83%98p%29+%EF%83%99+%28%EF%83%98q%29%5D+p+q+%EF%81%BEp+%EF%81%BEq+%28p%EF%83%9Aq%29+%28%EF%81%BEp%EF%83%99%EF%81%BEq%29+%28p%EF%83%9Aq%29%EF%83%9A%28%EF%81%BEp+%EF%83%99+%EF%81%BEq%29+B+B+S+S.jpg "(pq) [(p) (q)] p q p q (pq) (pq) (pq)(p q) B B S S")
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(pq) [(p) (q)] p q p q (pq) (pq) (pq)(p q) B B S S
![(pq) [(p) (q)] p q p q (pq) (pq) (pq)(p q) B B S S](http://slideplayer.info/slide/2898865/10/images/8/%28p%EF%83%9Aq%29+%EF%83%9A+%5B%28%EF%83%98p%29+%EF%83%99+%28%EF%83%98q%29%5D+p+q+%EF%81%BEp+%EF%81%BEq+%28p%EF%83%9Aq%29+%28%EF%81%BEp%EF%83%99%EF%81%BEq%29+%28p%EF%83%9Aq%29%EF%83%9A%28%EF%81%BEp+%EF%83%99+%EF%81%BEq%29+B+B+S+S.jpg "(pq) [(p) (q)] p q p q (pq) (pq) (pq)(p q) B B S S")
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(pq) [(p) (q)] p q p q (pq) (pq) (pq)(p q) B B S S
![(pq) [(p) (q)] p q p q (pq) (pq) (pq)(p q) B B S S](http://slideplayer.info/slide/2898865/10/images/9/%28p%EF%83%9Aq%29+%EF%83%9A+%5B%28%EF%83%98p%29+%EF%83%99+%28%EF%83%98q%29%5D+p+q+%EF%81%BEp+%EF%81%BEq+%28p%EF%83%9Aq%29+%28%EF%81%BEp%EF%83%99%EF%81%BEq%29+%28p%EF%83%9Aq%29%EF%83%9A%28%EF%81%BEp+%EF%83%99+%EF%81%BEq%29+B+B+S+S.jpg "(pq) [(p) (q)] p q p q (pq) (pq) (pq)(p q) B B S S")
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(pq) [(p) (q)] p q p q (pq) (pq) (pq) (p q) B B B S
![(pq) [(p) (q)] p q p q (pq) (pq) (pq) (p q) B B B S](http://slideplayer.info/slide/2898865/10/images/10/%28p%EF%83%9Aq%29+%EF%83%99+%5B%28%EF%83%98p%29+%EF%83%99+%28%EF%83%98q%29%5D+p+q+%EF%81%BEp+%EF%81%BEq+%28p%EF%83%9Aq%29+%28%EF%81%BEp%EF%83%99%EF%81%BEq%29+%28p%EF%83%9Aq%29+%EF%83%99%28%EF%81%BEp+%EF%83%99+%EF%81%BEq%29+B+B+B+S.jpg "(pq) [(p) (q)] p q p q (pq) (pq) (pq) (p q) B B B S")
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(pq) [(p) (q)] p q p q (pq) (pq) (pq) (p q) B B S B
![(pq) [(p) (q)] p q p q (pq) (pq) (pq) (p q) B B S B](http://slideplayer.info/slide/2898865/10/images/11/%28p%EF%83%9Aq%29+%EF%83%99+%5B%28%EF%83%98p%29+%EF%83%99+%28%EF%83%98q%29%5D+p+q+%EF%81%BEp+%EF%81%BEq+%28p%EF%83%9Aq%29+%28%EF%81%BEp%EF%83%99%EF%81%BEq%29+%28p%EF%83%9Aq%29+%EF%83%99%28%EF%81%BEp+%EF%83%99+%EF%81%BEq%29+B+B+S+B.jpg "(pq) [(p) (q)] p q p q (pq) (pq) (pq) (p q) B B S B")
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(pq) [(p) (q)] p q p q (pq) (pq) (pq) (p q) B B S S
![(pq) [(p) (q)] p q p q (pq) (pq) (pq) (p q) B B S S](http://slideplayer.info/slide/2898865/10/images/12/%28p%EF%83%9Aq%29+%EF%83%9A+%5B%28%EF%83%98p%29+%EF%83%99+%28%EF%83%98q%29%5D+p+q+%EF%81%BEp+%EF%81%BEq+%28p%EF%83%9Aq%29+%28%EF%81%BEp%EF%83%99%EF%81%BEq%29+%28p%EF%83%9Aq%29+%EF%83%99%28%EF%81%BEp+%EF%83%99+%EF%81%BEq%29+B+B+S+S.jpg "(pq) [(p) (q)] p q p q (pq) (pq) (pq) (p q) B B S S")
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(pq) [(p) (q)] p q p q (pq) (pq) (pq) (p q) B B S S
![(pq) [(p) (q)] p q p q (pq) (pq) (pq) (p q) B B S S](http://slideplayer.info/slide/2898865/10/images/13/%28p%EF%83%9Aq%29+%EF%83%9A+%5B%28%EF%83%98p%29+%EF%83%99+%28%EF%83%98q%29%5D+p+q+%EF%81%BEp+%EF%81%BEq+%28p%EF%83%9Aq%29+%28%EF%81%BEp%EF%83%99%EF%81%BEq%29+%28p%EF%83%9Aq%29+%EF%83%99%28%EF%81%BEp+%EF%83%99+%EF%81%BEq%29+B+B+S+S.jpg "(pq) [(p) (q)] p q p q (pq) (pq) (pq) (p q) B B S S")
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(pq) [(p) (q)] p q p q (pq) (pq) (pq) (p q) B B S S
![(pq) [(p) (q)] p q p q (pq) (pq) (pq) (p q) B B S S](http://slideplayer.info/slide/2898865/10/images/14/%28p%EF%83%9Aq%29+%EF%83%9A+%5B%28%EF%83%98p%29+%EF%83%99+%28%EF%83%98q%29%5D+p+q+%EF%81%BEp+%EF%81%BEq+%28p%EF%83%9Aq%29+%28%EF%81%BEp%EF%83%99%EF%81%BEq%29+%28p%EF%83%9Aq%29+%EF%83%99%28%EF%81%BEp+%EF%83%99+%EF%81%BEq%29+B+B+S+S.jpg "(pq) [(p) (q)] p q p q (pq) (pq) (pq) (p q) B B S S")
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(pq) [(p) (q)] p q p q (pq) (pq) (pq) (p q) B B S S
![(pq) [(p) (q)] p q p q (pq) (pq) (pq) (p q) B B S S](http://slideplayer.info/slide/2898865/10/images/15/%28p%EF%83%9Aq%29+%EF%83%99+%5B%28%EF%83%98p%29+%EF%83%99+%28%EF%83%98q%29%5D+p+q+%EF%81%BEp+%EF%81%BEq+%28p%EF%83%9Aq%29+%28%EF%81%BEp%EF%83%99%EF%81%BEq%29+%28p%EF%83%9Aq%29+%EF%83%99%28%EF%81%BEp+%EF%83%99+%EF%81%BEq%29+B+B+S+S.jpg "(pq) [(p) (q)] p q p q (pq) (pq) (pq) (p q) B B S S")
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(pq) [(p) (q)] p q p q (pq) (pq) (pq) (p q) B B S S B S S B S S B B S S S B B S B S S S S B B S B S Karena (pq) [(p) (q)] selalu ber-nilai SALAH untuk setiap nilai p dan q maka (pq) [(p) (q)] disebut dengan KOTRADIKSI.
![(pq) [(p) (q)] p. q. p. q. (pq) (pq) (pq) (p q) B. B. S. S. B. S. S.](http://slideplayer.info/slide/2898865/10/images/16/%28p%EF%83%9Aq%29+%EF%83%99+%5B%28%EF%83%98p%29+%EF%83%99+%28%EF%83%98q%29%5D+p.+q.+%EF%81%BEp.+%EF%81%BEq.+%28p%EF%83%9Aq%29+%28%EF%81%BEp%EF%83%99%EF%81%BEq%29+%28p%EF%83%9Aq%29+%EF%83%99%28%EF%81%BEp+%EF%83%99+%EF%81%BEq%29+B.+B.+S.+S.+B.+S.+S..jpg "B. S. S. B. B. S. S. S. B. B. S. B. S. S. S. S. B. B. S. B. S. Karena (pq) [(p) (q)] selalu ber-nilai SALAH untuk setiap nilai p dan q maka (pq) [(p) (q)] disebut dengan KOTRADIKSI.")
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[(pq) r] p P Q R (PQ) [(PQ)R] [(PQ)R]P B B B B B S B S B B
![[(pq) r] p P Q R (PQ) [(PQ)R] [(PQ)R]P B B B B B S B S B B](http://slideplayer.info/slide/2898865/10/images/17/%5B%28p%EF%83%99q%29+%EF%83%9E+r%5D+%EF%83%9E+p+P+Q+R+%28P%EF%83%99Q%29+%5B%28P%EF%83%99Q%29%EF%83%9ER%5D+%5B%28P%EF%83%99Q%29%EF%83%9ER%5D%EF%83%9EP+B+B+B+B+B+S+B+S+B+B.jpg "[(pq) r] p P Q R (PQ) [(PQ)R] [(PQ)R]P B B B B B S B S B B")
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[(pq) r] p P Q R (PQ) [(PQ)R] [(PQ)R]P B B B B B B S B B S
![[(pq) r] p P Q R (PQ) [(PQ)R] [(PQ)R]P B B B B B B S B B S](http://slideplayer.info/slide/2898865/10/images/18/%5B%28p%EF%83%99q%29+%EF%83%9E+r%5D+%EF%83%9E+p+P+Q+R+%28P%EF%83%99Q%29+%5B%28P%EF%83%99Q%29%EF%83%9ER%5D+%5B%28P%EF%83%99Q%29%EF%83%9ER%5D%EF%83%9EP+B+B+B+B+B+B+S+B+B+S.jpg "[(pq) r] p P Q R (PQ) [(PQ)R] [(PQ)R]P B B B B B B S B B S")
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[(pq) r] p P Q R (PQ) [(PQ)R] [(PQ)R]P B B B B B B B S B S
![[(pq) r] p P Q R (PQ) [(PQ)R] [(PQ)R]P B B B B B B B S B S](http://slideplayer.info/slide/2898865/10/images/19/%5B%28p%EF%83%99q%29+%EF%83%9E+r%5D+%EF%83%9E+p+P+Q+R+%28P%EF%83%99Q%29+%5B%28P%EF%83%99Q%29%EF%83%9ER%5D+%5B%28P%EF%83%99Q%29%EF%83%9ER%5D%EF%83%9EP+B+B+B+B+B+B+B+S+B+S.jpg "[(pq) r] p P Q R (PQ) [(PQ)R] [(PQ)R]P B B B B B B B S B S")
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[(pq) r] p P Q R (PQ) [(PQ)R] [(PQ)R]P B B B B B B B B S B
![[(pq) r] p P Q R (PQ) [(PQ)R] [(PQ)R]P B B B B B B B B S B](http://slideplayer.info/slide/2898865/10/images/20/%5B%28p%EF%83%99q%29+%EF%83%9E+r%5D+%EF%83%9E+p+P+Q+R+%28P%EF%83%99Q%29+%5B%28P%EF%83%99Q%29%EF%83%9ER%5D+%5B%28P%EF%83%99Q%29%EF%83%9ER%5D%EF%83%9EP+B+B+B+B+B+B+B+B+S+B.jpg "[(pq) r] p P Q R (PQ) [(PQ)R] [(PQ)R]P B B B B B B B B S B")
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[(pq) r] p P Q R (PQ) [(PQ)R] [(PQ)R]P B B B B B B B B S B
Karena [(pq) r] p bisa bernilai BENAR atau SALAH untuk setiap nilai p dan q maka pernyataan [(pq) r] p disebut dengan KONTIGENSI.
![[(pq) r] p P Q R (PQ) [(PQ)R] [(PQ)R]P B B B B B B B B S B](http://slideplayer.info/slide/2898865/10/images/21/%5B%28p%EF%83%99q%29+%EF%83%9E+r%5D+%EF%83%9E+p+P+Q+R+%28P%EF%83%99Q%29+%5B%28P%EF%83%99Q%29%EF%83%9ER%5D+%5B%28P%EF%83%99Q%29%EF%83%9ER%5D%EF%83%9EP+B+B+B+B+B+B+B+B+S+B.jpg "Karena [(pq) r] p bisa bernilai BENAR atau SALAH untuk setiap nilai p dan q maka pernyataan [(pq) r] p disebut dengan KONTIGENSI.")
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