For S:((P Q) R)((P Q)(Q R)), choose the correct statements.

S is neither a tautology nor a contradiction

GATE 2021 CS (CS2) – Question 25

Engineering Mathematics · Discrete Mathematics: Propositional and First Order Logic · 1 mark · Multiple select

For $S:((P\land Q)\to R)\to((P\land Q)\to(Q\to R))$, choose the correct statements.

S is neither a tautology nor a contradiction
S is a tautology
S is a contradiction
The antecedent and consequent of S are logically equivalent

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Show answer and explanation

Correct answer: (B) S is a tautology; (D) The antecedent and consequent of S are logically equivalent

Explanation

The antecedent simplifies to ¬P∨¬Q∨R. The consequent is ¬(P∧Q)∨(¬Q∨R), simplifying to the same expression. Thus D holds, and an implication from a proposition to an equivalent proposition is always true, proving B. Select B,D.

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