If statement1 is 'If A then B' and statement2 is 'B is false.' What can be inferred about A?

If statement1 is 'If A then B' and statement2 is 'B is false.' What can be inferred about A?

• A. A is false
• B. A is true
• C. B is true
• D. A implies not B

Answer: (A)

This uses a basic logical rule called modus tollens. If A implies B and B is false, then A cannot be true; in other words, A must be false. The reasoning is straightforward: if A were true, B would have to be true as a consequence of the implication, but since B is not true, A cannot hold. A helpful way to see it is to think of the contrapositive: If not B, then not A. Since B is false, not B is true, so not A must be true. Therefore A is false.

This uses a basic logical rule called modus tollens. If A implies B and B is false, then A cannot be true; in other words, A must be false. The reasoning is straightforward: if A were true, B would have to be true as a consequence of the implication, but since B is not true, A cannot hold.

A helpful way to see it is to think of the contrapositive: If not B, then not A. Since B is false, not B is true, so not A must be true. Therefore A is false.