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@suissa
Created May 10, 2020 02:18
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3) Determinar o valor lógico, quando possível, de cada uma das proposições a seguir, mostre o desenvolvimento completo para encontrar a resposta:
a) (r ^ (~q > p)) ^ ~((p <> ~q) > r v ~p)
sabendo que V(p) = F e V(r) = V
(v ^ (~q > F)) ^ ~((F <> ~q) > v v ~F)
(v ^ (~q > F)) ^ ~((F <> ~q) > v v ~F)
q = V
(v ^ (~V > F)) ^ ~((F <> ~V) > v v ~F)
(v ^ (F > F)) ^ ~((F <> F) > v v V)
(v ^ (F > F)) ^ ~((F <> F) > V)
(v ^ (V)) ^ ~((V) > V)
(v ^ (V)) ^ ~(V)
(V ^ F)
(F)
q = F
(v ^ (~F > F)) ^ ~((F <> ~F) > v v ~F)
(v ^ (V > F)) ^ ~((F <> V) > v v V)
(v ^ (V > F)) ^ ~((F <> V) > V)
(v ^ (F)) ^ ~((F) > V)
(F) ^ ~(F)
(F ^ V)
(F)
b) p <> q > p v ~r
sabendo que V(p) = F e V(r) = F
c) (p v q) ^ ~r
sabendo que V(p) = V e V(r) = V
(V v q) ^ ~V
q = V
(V v V) ^ F
V ^ F
F
q = F
(V v F) ^ F
V ^ F
F
d) (p > ~q) ^ (~p ^ r)
sabendo que V(q) = F e V(r) = V
p = V
(p > ~V) ^ (~p ^ V)
(V > F) ^ (F ^ V)
(V > F) ^ ~(F > ~V) // equivalência lógica do E/ ^
(V > F) ^ ~(F > F)
(V > F) ^ ~(V)
(F) ^ (F)
(F)
p = F
(p > ~V) ^ (~p ^ V)
(F > F) ^ (~F ^ V)
(V) ^ (V)
(V)
> = condicional
<>=bicondicional
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