Logical table of P->Q math statements

Question

In a course I had, we have been given two statements P and Q and their "boolean table" :

While I completely understand P and Q and P or Q values, I can't understand the first two lines for P->Q, why is the result true even when P is false ?

Thank you.

Answer 1

Think of it this way. If $P$ is true, we test $P \rightarrow Q$ by seeing whether $Q$ is true or not.

In other words $P\rightarrow Q$ is falsified when $P$ is true but $Q$ is false. If $P$ is not true, we can't do any such falisifying verification.

So if $P$ is false, then $P \rightarrow Q$ is ... not false.