Question

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

• A. Peacocks dance only when it is raining.
• B. When peacocks dance, it is raining.
• C. When peacocks are not dancing, it is not raining.
• D. When it is not raining, peacocks do not dance.

Hint:

For a statement "if P then Q", only the contrapositive "if not Q then not P" is guaranteed to be true, not the converse or inverse.

Answer 1

The Correct Option is C

The sentence "when it is raining, peacocks dance" is a plain if-then rule: raining leads to dancing. It does not say dancing only happens because of rain, and it does not say anything directly about what happens when it stops raining. To find what must be true, we test each option against this rule.

1. Peacocks dance only when it is raining: this would mean dancing never happens without rain, but the original sentence only tells us rain causes dancing, not that dancing has no other cause, so this is not forced to be true.
2. When peacocks dance, it is raining: this again reverses the original rule and claims dancing always signals rain, which the sentence does not guarantee.
3. When peacocks are not dancing, it is not raining: if it were raining while peacocks were not dancing, the original rule would be broken, since rain is supposed to lead to dancing. So no dancing means it cannot be raining, and this option must be true.
4. When it is not raining, peacocks do not dance: the original sentence says nothing about peacocks on days without rain, they could still dance for some other reason, so this is not guaranteed.

Only the third option follows directly from the original rule without adding any new assumption, so it is the one that is necessarily true.

Let's summarize:

• "Raining implies dancing" only guarantees its contrapositive, "not dancing implies not raining".
• The converse and inverse of a conditional statement are not automatically true.

So the correct option is "When peacocks are not dancing, it is not raining."