Implication

“If $P$ then $Q$” is written $P \Rightarrow Q$. $P$ is the hypothesis and $Q$ is the conclusion.

The implication is false in exactly one case: $P$ is true and $Q$ is false. In every other case it is true.

When $P$ is false, the implication is true whatever $Q$ says. Mathematicians call this vacuously true.