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GATE 2026 CS (CS2) – Question 5

General Aptitude · Analytical Aptitude: Logical Reasoning and Deduction · 1 mark · Multiple choice

'When it is raining, peacocks dance.' Based only on this sentence, which one of the following options is necessarily true?

  1. Peacocks dance only when it is raining.
  2. When peacocks dance, it is raining.
  3. When peacocks are not dancing, it is not raining.
  4. When it is not raining, peacocks do not dance.

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Show answer and explanation

Correct answer: (C) When peacocks are not dancing, it is not raining.

Explanation

Let $P$ denote "it is raining" and $Q$ denote "peacocks dance". The given sentence is $P \to Q$. Its contrapositive is $\neg Q \to \neg P$, which reads: if peacocks are not dancing, then it is not raining. The converse and inverse are not guaranteed. Therefore, option (C) is necessarily true.