Sets, Relation and Functions

Let, $(c, a )$ a element of $(S \circ R)^-1$ where $c \in C$ and $a \in A$ .

So, $(c, a)\in (S \circ R)^-1 \iff (a, c) \in S \circ R$ $\iff \exists b \in B: (a, b) \in R \quad and \quad (b, c) \in S$ $\iff \exists b \in B : (b, a) \in R^-1 \quad and \quad (c, b) \in S^-1$ $\iff \exists b \in B : (c, b) \in S^-1 \quad and \quad (b, a) \in R^-1$ $\iff (c, a) \in R^-1 \circ S^-1$

Hence, $(S \circ R)^-1 = R^-1 \circ S^-1$ .