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

Let $P$ represent "it is raining" and $Q$ represent "peacocks dance".

The given statement is of the form:

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

Translating the contrapositive into English gives: "When peacocks are not dancing, it is not raining."

Evaluating the other options:

• A and B represent the converse $Q \implies P$, which is a logical fallacy and not necessarily true.

• D represents the inverse $

eg P \implies eg Q$, which is also a logical fallacy.

Therefore, option C is the correct answer.