Originally Posted by

**Mush** Hello.

Having a bit of trouble understanding the truth table for the statement:

$\displaystyle P \to Q $.

Could somebody run me through the scenarios and explain how they affect the truth value of $\displaystyle P \to Q $. In particular, the scenario where $\displaystyle P$ is false, but $\displaystyle Q$ is true... how does this imply that $\displaystyle P \to Q $ is true?

So :

$\displaystyle P$ true, $\displaystyle Q$ true: $\displaystyle P \to Q $?

$\displaystyle P$ true, $\displaystyle Q$ false: $\displaystyle P \to Q $?

$\displaystyle P$ false, $\displaystyle Q$ true: $\displaystyle P \to Q $?

$\displaystyle P$ false, $\displaystyle Q$ false: $\displaystyle P \to Q $?

I know the answers are true, false, true, true. But can someone explain the logic behind it?