I have difficulties understanding why $ P \implies Q$ is equivalent to P only if Q. I do understand that in the statement "P only if Q", it means if $ \lnot Q \implies \lnot P$".
Regarding this example, Equivalence of $a \rightarrow b$ and $\lnot a \vee b$
If I win the lottery, then I will give you \$1 billion. This statement has the form $P \implies Q$.
But saying P only if Q, means "I win the lottery only if I give you $1 billion" doesn't sound so right. Is there anything I'm missing here?