Exercise 8, § 6

Let $E$, $F$ be two sets, let $R$ be an equivalence relation on $F$, and let $f$ be a mapping of $E$ into $F$. If $S$ is the equivalence relation which is the inverse image of $R$ under $f$, and if $A = f\langle E \rangle$, define a canonical bijection of $E/S$ onto $A/R_A$.