Exercise 9, § 6

Let $F$, $G$ be two sets, let $R$ be an equivalence relation on $F$, let $p$ be the canonical mapping of $F$ onto $F/R$, and let $f$ be a surjection of $G$ onto $F/R$. Show that there exists a set $E$, a surjection $g$ of $E$ onto $F$, and a surjection $h$ of $E$ onto $G$, such that $p \circ g = f \circ h$.