Logica Matematica
Artigos Científicos: Logica Matematica. Pesquise 860.000+ trabalhos acadêmicosPor: miyabara • 15/11/2013 • 571 Palavras (3 Páginas) • 375 Visualizações
Sistemas de Informação Lógica Matemática
Universidade Federal de Mato Grosso (UFMT)
Crie a tabela verdade e indique se são equivalência
a) ~(~(P v Q)) ⇔ P v Q
P Q PvQ ~(PvQ) ~(~(PvQ) ~(~(PvQ) ⇔ PvQ
V V V F V V V V
V F V F V V V V
F V V F V V V V
F F F V F F F V
R: São equivalentes
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b) (P v Q) ^ ~R ⇔ ~R ^ (P v Q)
P Q R PvQ ~R (PvQ)^~R ~R ^ PvQ (P v Q) ^ ~R ⇔ ~R ^ (P v Q)
V V V V F F F V F F F V
V V F V V V V V V V V V
V F V V F F F V F F F V
V F F V V V V V V V V V
F V V V F F F V F F F V
F V F V V V V V V V V V
F F V F F F F F F F F V
F F F F V F V F F F F V
R: São equivalentes
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c) [P → (Q ↔ R)] v [P → (Q ↔ R)] ⇔ [P → (Q ↔ R)]
P Q R Q ↔ R [P → (Q ↔ R)] [P → (Q ↔ R)] v [P → (Q ↔ R)]
V V V V V V V V
V V F F F F F F
V F V F F F F F
V F F V V V V V
F V V V V V V V
F V F F V V V V
F F V F V V V V
F F F V V V V V
[P → (Q ↔ R)] v [P → (Q ↔ R)] ⇔ [P → (Q ↔ R)]
V V V
F F V
F F V
V V V
V V V
V V V
V V V
V V V
R: São equivalentes
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d) ~(~(~P)) ⇔ ~P
P ~P ~(~P) ~(~(~P) ~(~(~P) ⇔ ~P
V F V F F F V
F V F V V V V
V F V F F F V
F V F V V V V
R: São equivalentes
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e) P ^ (Q → R) ⇔ (Q → R) ^ P
P Q R Q → R P ^ (Q → R) Q → R ^ P P ^ (Q → R) ⇔ (Q → R) ^ P
V V V V V V V V V V V
V V F F F F V F F F V
V F V V V V V V V V V
V F F V V V V V V V V
F V V V F V F F F F V
F V F F F F F F F F V
F F V V F V F F F F V
F F F V F V F F F F V
R: São equivalentes
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f) ~P → (Q ^ S) ⇔ ~(Q ^ S) → P
P Q S ~P (Q ^ S) ~P → (Q ^ S) (Q ^ S) ~(Q ^ S) P ~(Q ^ S) → P ~P → (Q ^ S) ⇔ ~(Q ^ S) → P
V V V F V V V F V V V V V
V V F F F V F V V V V V V
V F V F F V F V V V V V V
V F F F F V F V V V V V V
F V V V V V V F F V V V V
F V F V F F F V F F F F V
F F V V F F F V F F F F V
F F F V F F F V F F F F V
R: São equivalentes
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g) (P → ~Q) ^ (~R ^ S) ⇔ [(P → ~Q) ^ ~R] ^ S
P Q R S ~Q (P → ~Q) ~R (~R^S) (P → ~Q) ^ (~R ^ S) (P → ~Q) ~R P → ~Q) ^ ~R S [(P → ~Q) ^ ~R] ^ S
V V V V F F F F F F F F V F
V V V F F F F F F F F F F F
V V F V F F V V F F V F V F
V V F F F F V F F F V F F F
V F V V V V F F F V F F V F
V F V F V V F F F V F F F F
V F F V V V V V V V V V V V
V F F F V V V F F V V V F F
F V V V F V F F F V F F V F
F V V F F V F F F V F F F F
F V F V F V V V V V V V V V
F V F F F V V F F V V V F F
F F V V V V F F F V F F V F
F F V F V V F F F V F F F F
F F F V V V V V V V V V V V
F F F F V V V F F V V V F F
(P → ~Q) ^ (~R ^ S) ⇔ [(P → ~Q) ^ ~R] ^ S
F F V
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