GATE 2012 CS (CS1) – Question 11

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

I₁: If it rains, the cricket match will not be played; the match was played; infer no rain. I₂: If it rains, the match will not be played; it did not rain; infer the match was played. Which is true?

Both inferences correct
I₁ correct, I₂ incorrect
I₁ incorrect, I₂ correct
Both incorrect

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Show answer and explanation

Correct answer: (B) I₁ correct, I₂ incorrect

Explanation

Let R mean rain and P mean match played. The premise R→¬P has contrapositive P→¬R, so I₁ is valid. From ¬R no conclusion about P follows: other causes can cancel the match. I₂ denies the antecedent. Thus B.

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