If A -> B and B -> A, what is true about A and B?

• A. A and B have the same truth value
• B. A is always true
• C. B is always true
• D. A implies not B

Answer: (A)

A and B are logically equivalent. Having A → B and B → A means each statement guarantees the other. If A is true, the first implication forces B to be true, and then the second implication holds as well. If A is false, the first implication is still true, but the second implies that B cannot be true (otherwise B → A would fail), so B must also be false. The only possibilities are both true or both false, so they share the same truth value.