Definition 5.1.2 (Composition). Let $X$ be a set and $U, V \subset X \times X$, then the composition of $U$ and $V$ is the set
\[U \circ V = \bracs{(x, z) \in X \times X| \exists y \in Y: (x, y) \in U, (y, z) \in V}\]
Definition 5.1.2 (Composition). Let $X$ be a set and $U, V \subset X \times X$, then the composition of $U$ and $V$ is the set