Exercise 4, § 5

Let $A$ and $B$ be two sets. For every subset $G$ of $A \times B$ let $\tilde{G}$ be the graph of the mapping $x \mapsto G\langle\{x\}\rangle$ from $A$ into $\mathfrak{P}(B)$. Now prove that the mapping $G \mapsto \tilde{G}$ is a bijection of $\mathfrak{P}(A \times B)$ onto $(\mathfrak{P}(B))^A$.