Prueba de escritorio

PRUEBA DE ESCRITORIO

S ≡ {{P, Q, R},  {¬P},  {P, Q, R}, {P, ¬Q}}

S ≡ {{P, Q, R}, {¬P}, {P, Q, R}, {P, ¬Q}, R1 (C1, C2) {Q, R}}

S ≡ {{P, Q, R}, {¬P}, {P, Q, R}, {P, ¬Q}, R1 (C1, C2) {Q, R}, R2 (C1, C4) {P, R}}

S ≡ {{P, Q, R}, {¬P}, {P, Q, R}, {P, ¬Q}, R1 (C1, C2) {Q, R}, R2 (C1, C4) {P, R}, R3 (C2, C4) {¬Q}}

S ≡ {{P, Q, R}, {¬P}, {P, Q, R}, {P, ¬Q}, R1 (C1, C2) {Q, R}, R2 (C1, C4) {P, R}, R3 (C2, C4) {¬Q}, R4 (C5,  C7) {R}}

CONSISTENTE

tablas de verdad

1)

p	^	q	^	¬	r	v	¬q	^	¬p	→	r
1	1	1	0	0	1	1	0	0	0	1	1
1	1	1	1	1	0	0	0	1	0	1	0
1	0	0	0	0	1	1	1	0	0	1	1
1	0	0	0	0	0	1	1	0	0	1	0
0	0	1	0	0	1	1	0	0	1	1	1
0	0	1	0	1	0	0	0	0	1	0	0
0	0	0	0	0	1	1	1	0	1	1	1
0	0	0	0	0	0	1	1	0	1	0	0

es satisfactible.
2)

p	r	P →(p v q)	P v q	P → q	(p v q) ^  (p →q)	P v ¬q	(p → q) →(p ^ q)	P ↔ q	(p ^ q)	(p → q) → ¬p	[( p → q) →¬p] ^ ( p v q)	[(p→ q) → (p ^ q) ]→ ¬p	(¬p ^ q)	(p v q) → ¬q	(p v ¬q )  (p ↔ q)	¬p ^ ¬q	(p ^ q) ^ [(p → q)→ ¬p]
1	1	1	1	1	1	1	1	1	1	0	0	0	0	0	0	0	0
0	1	1	1	1	1	0	0	0	0	1	1	1	1	0	0	0	0
1	0	1	1	0	0	1	1	0	0	1	1	0	0	1	1	0	0
0	0	1	0	1	0	1	0	1	0	1	0	1	0	1	0	1	0