If P implies Q and Q is false, what can we conclude about P?

• A. P is true
• B. No conclusion
• C. P is false
• D. P is both true and false

Answer: (C)

In logic, a statement of the form “if P then Q” is true when either P is false or Q is true. If Q is false, the only way for the implication to stay true is if P is also false; otherwise, having P true would force Q to be true, which contradicts Q being false. So P must be false.

This aligns with the idea that a true conditional cannot have its consequent fail when the antecedent is actually happening.