The following propositional statement is
(P → (Q v R)) → ((P ^ Q) → R)
(A)
satisfiable but not valid
(B)
valid
(C)
a contradiction
(D)
none of the above
Answer: (A)
Explanation:
The correct option is A Satisfiable but not valid
(P→(Q∨R))→((P∧Q)→R
≡(P→Q+R)→(PQ→R)
≡[P′+Q+R]→[(PQ)′+R]
≡[P′+Q+R]→[P′+Q′+R]
≡(P′+Q+R)′+P′+Q′+R
≡PQ′R′+P′+Q′+R
≡Q′+Q′PR′+P′+R
≡Q′+P′+R (by absorption law)
Which is a contingency (i.e. satisfiable but not valid).
Quiz of this Question
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