Composite relation

Given relations from set \(A\) to \(B\) and from \(B\) to \(C\), a composite relation is some relation from \(A\) to \(C\).

Define relation \(R\) from \(A\) to \(B\), relation \(S\) from \(B\) to \(C\). The composite of \(R\) and \(S\) is: $$ S \circ R = { (a, c) | (\exists b \in B) (a, b) \in R \land (b, c) \in S } $$