Step 1: Restating with Simple Variables:
Let R represent the event it is raining and D represent the event peacocks dance. The given sentence says $R \Rightarrow D$, meaning whenever R happens, D must also happen. Nothing is said about what happens when R does not happen, so we must be careful not to assume anything extra beyond this one directional link.
Step 2: Testing Each Option With a Scenario Check:
A good way to test logical statements is to imagine a scenario where the original statement $R \Rightarrow D$ holds true, but peacocks also dance for some completely unrelated reason, such as during a live music performance with no rain at all, and see which options break under this scenario.
Step 3: Detailed Explanation:
In our test scenario, suppose peacocks dance both when it rains and separately during music performances with no rain. Option (A), which claims peacocks dance only when it rains, is broken by this scenario, since here peacocks dance without rain too, so option (A) is not guaranteed.
Option (B), when peacocks dance, it is raining, is also broken by the same scenario, because peacocks are dancing during the music performance while it is not raining, so option (B) cannot be relied upon either.
Option (D), when it is not raining, peacocks do not dance, again fails in this scenario since peacocks are shown dancing without rain during the performance, so this option is also not necessarily true.
Option (C), when peacocks are not dancing, it is not raining, still holds up under this scenario and under every other possible scenario consistent with $R \Rightarrow D$, because if it ever rained while peacocks were not dancing, that would directly contradict the original statement that rain always causes dancing. So the absence of dancing always forces the absence of rain, matching exactly with the contrapositive $\text{not } D \Rightarrow \text{not } R$.
Final Answer:
Testing with a scenario where peacocks dance for reasons other than rain confirms that only option (C), the contrapositive statement, remains true in every case.
$\boxed{\text{When peacocks are not dancing, it is not raining.}}$