Question:medium

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

Show Hint

Find the contrapositive of the given conditional statement.
Updated On: Jul 28, 2026
  • 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.
Show Solution

The Correct Option is C

Solution and Explanation

Read the sentence as a rule: rain always brings out dancing peacocks, but the sentence never says dancing needs rain, and it never says no rain means no dancing. Test each option against a scenario where the rule still holds but peacocks dance for another reason, such as a nearby drum performance.

  1. Peacocks dance only when it is raining: fails, because peacocks could also dance for the drum performance without any rain, so this option does not have to be true.
  2. When peacocks dance, it is raining: fails for the same reason, dancing does not force rain.
  3. When peacocks are not dancing, it is not raining: this must hold, because if it were raining the rule guarantees dancing, so no dancing rules out rain every time.
  4. When it is not raining, peacocks do not dance: fails, since the drum-performance scenario has no rain but still has dancing.

Only the statement in option (C) survives every scenario consistent with the sentence, so it is the one that is necessarily true.

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