What does P <-> Q being true imply about P and Q?

• A. They have the same truth value.
• B. P is always true.
• C. Q is always false.
• D. They are independent.

Answer: (A)

P if and only if Q is true exactly when P and Q have the same truth value in every possible situation. In other words, the biconditional is true only when both P and Q are true together or both are false together. That’s why the statement implies they mirror each other. If P is true and Q is false, or P is false and Q is true, the biconditional would be false. So the best interpretation is that P and Q share the same truth value. The other ideas—P always true, Q always false, or P and Q being independent—don’t capture that requirement that P and Q must align in truth value for the biconditional to hold.