Answer
Shown below.
Work Step by Step
Let $E$ and $F$ be events. Then $P(E\cup F)=P(E)+P(F)-P(E\cap F)$ so $P(E\cap F)=P(E)+P(F)-P(E\cup F)$. As $P(E\cup F)$ decreases, $P(E\cap F)$ strictly increases; the maximum of $P(E\cup F)$ is 1, so $P(E\cap F)\geq P(E)+P(F)-1$.
