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GATE | GATE-CS-2004 | Question 70

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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).
 


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Last Updated : 11 Oct, 2021
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