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Consider the following two statements. Statement A: All physicians whose licenses have been revoked are physicians ineligible to practise. Statement B: All physicians eligible to practise are physicians whose licenses are intact. Which of the following is true with regard to the above two statements?

AStatement B is the contrapositive of Statement A and these statements are not logically equivalent
BStatement B is the contrapositive of Statement A and these two statements are logically equivalent ✓ Correct
CStatement B is the converse of Statement A and these two statements are not logically equivalent
DStatement B is the obverse of Statement A and these two statements are not logically equivalent
Correct answer: (B) Statement B is the contrapositive of Statement A and these two statements are logically equivalent
Explanation

Statement 2 is the contrapositive of Statement 1, and the two are logically equivalent.

Statement 1 says all physicians with revoked licences are ineligible to practise.

Contraposition negates both terms and exchanges their places.

Negating and swapping gives that all eligible physicians are those with intact licences.

This is exactly Statement 2, so it is the contrapositive of Statement 1.

For a universal affirmative, the contrapositive always keeps the same truth value.

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