GATE CS 2026 Set 2 Q5 — General Aptitude

Let us represent the given statement using propositional logic:

• Let $P$ be the proposition: "It is raining"
• Let $Q$ be the proposition: "Peacocks dance"

The given statement, "When it is raining, peacocks dance", can be written as:

$$P \implies Q$$

In classical logic, a conditional statement $P \implies Q$ is logically equivalent to its contrapositive, which is:

$$\neg Q \implies \neg P$$

Translating the contrapositive back into English gives:

"When peacocks are not dancing, it is not raining."

Let us evaluate the given options:

• Option A: "Peacocks dance only when it is raining" represents $Q \implies P$ (Converse), which is not logically equivalent.
• Option B: "When peacocks dance, it is raining" represents $Q \implies P$ (Converse), which is not logically equivalent.
• Option C: "When peacocks are not dancing, it is not raining" represents $\neg Q \implies \neg P$ (Contrapositive), which is logically equivalent and therefore necessarily true.
• Option D: "When it is not raining, peacocks do not dance" represents $\neg P \implies \neg Q$ (Inverse), which is not logically equivalent.

Therefore, the correct option is C.