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3
KONTINGENSI
Kontingensi adalah suatu bentuk kalimat yang bernilai benar (True) dan salah (False) tidak peduli bagaimana pun nilai kebenaran masing-masing kalimat penyusunnya.
Contoh:
Tunjukkan apakah pernyataan berikut ini tautologi, kontradiksi atau kontingensi.
1. (p q) [( p) ( q)]
2. (p q) [( p) ( q)]
3. [(p q) r] p
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[(p q) r] p
P
Q
R
(P Q)
[(P Q) R]
[(P Q) R] P
B
B
B
B
S
S
S
S
B
B
S
S
B
B
S
S
B
S
B
S
B
S
B
S
B
B
S
S
S
S
S
S
B
S
B
B
B
B
B
B
B
B
B
B
S
S
S
S
Karena [(p q) r] p bisa bernilai BENAR atau SALAH untuk setiap nilai p dan q maka pernyataan [(p q) r] p disebut dengan KONTINGENSI.
1. a ^ ¬a
2. a v ¬a
3. a ^ a
4. ¬a v ¬a
5. (a ^ b) b
6. ((a b) v ¬b) ¬a
7. (¬ p ^ r) (¬ r p)
8. (a ^ b) ^ (¬a v ¬b)
9. (a b) v c
10. ¬(a ^ b) v ¬(c a)
11. (a ^ b) (c v b)
12. (a c) (¬a ¬ b)
13. (((a ¬(b v ¬c)) v ¬b) (a c)
14. ¬ ((¬ p r) v (p ¬ q)) ^ r
15. ((a b) ^ (b c)) (a c)
16. ((a b) v (b c)) (a c)
Tentukan Soal dibawah ini apakah termasuk Tautologi, kontradiksi, atau kontingen.
5
(p q) [( p) ( q)]
p
q
p
q
(p q)
( p q)
(p q) ( p q)
B
B
S
S
B
S
B
S
S
S
B
B
S
B
S
B
B
B
B
S
S
S
S
B
S
S
S
S
Karena (p q) [( p) ( q)] selalu ber-nilai SALAH untuk setiap nilai p dan q maka (p q) [( p) ( q)] disebut dengan KONTRADIKSI.
1
TAUTOLOGI, KONTRADIKSI
DAN CONTINGENT
Represented by:
Firmansyah,S.Kom.
4
(p q) [( p) ( q)]
p
q
p
q
(p q)
( p q)
(p q) ( p q)
B
B
S
S
B
S
B
S
S
S
B
B
S
B
S
B
B
B
B
S
S
S
S
B
B
B
B
B
Karena (p q) [( p) ( q)] selalu ber-nilai BENAR untuk setiap nilai p dan q maka (p q) [( p) ( q)] disebut dengan TAUTOLOGI.
2
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 kalimat yang selalu bernilai salah (False), tidak peduli bagaimanapun nilai kebenaran masing-masing kalimat penyusunnya.
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