When is the biconditional P <-> Q true?

• A. P and Q have the same truth value.
• B. P implies Q but Q does not imply P.
• C. P and Q are both false.
• D. P or Q is true.

Answer: (A)

P <-> Q is true exactly when P and Q share the same truth value. It says P is true if and only if Q is true, so their truth values must move together. If both P and Q are true, the biconditional holds; if both are false, it still holds. If one is true and the other false, the biconditional is false. This is why the correct description is that P and Q have the same truth value.