When P -> Q, why is it true when P is false and Q is true, but why is it false when P is true and Q is false? If I suppose P mean "Jon is a guy" and Q mean "Mary is a girl". When both P and Q are true it does make sense that this proposition is true because Jon is a guy and Mary is a girl, but when it come to the second and third agreement, where P is false but Q is true still make the proposition true, but the Proposition is a false when P is true and Q is false. I tried replacing P and Q with "Jon is a guy" and "Mary is a girl". And it doesn't make sense why do one of them is right and the another one is wrong? I believe this is not a smart question, but if there's anyone forgo their time to explain this I would be really appreciate. Thank you very much.