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GATE | GATE CS 2021 | Set 1 | Question 17

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  • Last Updated : 17 Sep, 2021

Let p and q be two propositions. Consider the following two formulae in propositional logic.

S1:  (¬p∧(p∨q))→q
S2:  q→(¬p∧(p∨q)) 

Which one of the following choices is correct?
(A) Both S1 and S2 are tautologies.
(B) S1 is a tautology but S2 is not a tautology
(C) S1 is not a tautology but S2 is a tautology
(D) Neither S1 nor S2 is a tautology

Answer: (B)

Explanation: S1: (¬p∧(p∨q))→q = p'(p+q) → q = p + p’q’ + q = p + q’ + q = p + true = Tautology

S2: q→(¬p∧(p∨q)) = q’ + p'(p+q) = q’ + p’q = q’ + p’ = (p.q)’ = Contingency

Contingency = neither tautology nor contradiction.

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