Correct : c

The correct answer is Option C — When peacocks are not dancing, it is not raining.
The given statement, "When it is raining, peacocks dance", is a conditional statement of the form R → D (Raining implies Dancing). In formal logic, only one transformation of a conditional is guaranteed to preserve its truth: the contrapositive.
The contrapositive of R → D is ¬D → ¬R — "If peacocks are not dancing, then it is not raining." This is logically equivalent to the original statement and is therefore necessarily true. This is Option C.
Option A — "Peacocks dance only when it is raining" (D → R): This is the converse of the original. The converse is not logically equivalent — peacocks could dance for reasons other than rain. Not necessarily true.
Option B — "When peacocks dance, it is raining" (D → R): Also the converse, same as Option A. Not necessarily true.
Option C — "When peacocks are not dancing, it is not raining" (¬D → ¬R): This is the contrapositive of the original, which is always logically equivalent to the original conditional. Necessarily true. Correct.
Option D — "When it is not raining, peacocks do not dance" (¬R → ¬D): This is the inverse of the original. Like the converse, the inverse is not logically equivalent — peacocks might still dance even when it is not raining. Not necessarily true.
The simple rule: of the four related conditionals (original, converse, inverse, contrapositive), only the contrapositive always shares the same truth value as the original.