GATE CS 2026 Set 2 Q.5: Analytical and Logical Reasoning

'When it is raining, peacocks dance.'

Based only on this sentence, which one of the following options is necessarily true?

Peacocks dance only when it is raining.

When peacocks dance, it is raining.

When peacocks are not dancing, it is not raining.

When it is not raining, peacocks do not dance.

Official answer and solution

Official answer: C
From: Official GATE 2026 answer key

Solution

Translate the conditional statement into propositional logic $R \rightarrow D$ and take its contrapositive $\neg D \rightarrow \neg R$ .

Let $R$ denote 'it is raining' and $D$ denote 'peacocks dance'. The given statement is the implication $R \rightarrow D$ . An implication is logically equivalent to its contrapositive $\neg D \rightarrow \neg R$ , which states: 'When peacocks are not dancing, it is not raining.' Converse ( $D \rightarrow R$ ) and inverse ( $\neg R \rightarrow \neg D$ ) are not necessarily true.

Final answer

Option (C)

Common trap

Confusing the converse ('When peacocks dance, it is raining') with the contrapositive.

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2026 Computer Science and Information Technology - Session 2 (CS2)
Question: 5 of 65
Section: General Aptitude

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