Why is the implication $P \Rightarrow Q$ false if and only if $P$ is true and $Q$ is false ?
Is this because if $P$ implies $Q$, where $P$ is true and $Q$ is false, then $Q$ is also true by definition of the implication ?
The exact definition of the implication $P \Rightarrow Q$: if $P$ then $Q$ is also true ?
So given an implication $P \Rightarrow Q$ where $P$ is true and $Q$ is false it must be false, since no true statement can never imply a false statement, since this would mean the false statement would be true, which it is not ?
