Let $A$ and $B$ be arbitrary non-empty sets and let $F\colon A\to P(B)$, be an arbitrary function which covers $B$ in the sense that $\forall b \in B$, $\exists a \in A$ such that $b \in F(a)$ holds.
Using axiom of choice show there exists a function $G: B \rightarrow A$ ,such that for all $b\in B$, $b \in F(G(b))$