If P → Q, and Q is true, which statement about P is correct?

• A. P is true
• B. P is false
• C. P could be true or false
• D. P is necessarily false

Answer: (C)

Knowing that a conditional P → Q is true means that if P happens, Q must happen, but it does not guarantee that P did happen. If Q is true, P could have happened or not; both possibilities are consistent with P → Q being true. For example, if P is “it is raining” and Q is “the ground is wet,” then P → Q can be true even if it didn’t rain (the ground could be wet for another reason), or if it did rain (which would make P true). Therefore, the truth of Q does not determine P, so P could be true or false.