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:

Find the contrapositive of the given conditional statement.

Answer 1

The Correct Option is C

The sentence "When it is raining, peacocks dance" is a conditional of the form "if it is raining, then peacocks dance." Let R stand for "it is raining" and D stand for "peacocks dance," so the statement is R implies D. Only the logically equivalent form of this statement, its contrapositive, is guaranteed to be true.

1. Peacocks dance only when it is raining: this claims D implies R, which reverses the original statement. Peacocks could dance for other reasons too, so this is not guaranteed.
2. When peacocks dance, it is raining: this is the same reversed claim, D implies R, and is not forced by the original sentence.
3. When peacocks are not dancing, it is not raining: this says not D implies not R, which is exactly the contrapositive of R implies D, so it must be true whenever the original statement is true.
4. When it is not raining, peacocks do not dance: this says not R implies not D, which is again the reverse direction and does not follow from the sentence.

Since only the contrapositive is logically forced by the given sentence, option (C) is the answer.