Let \(\mathcal{R}_2 \circ \mathcal{R}_1 \subseteq S_1 \times S_3\) be the composite of the two relations \(\mathcal{R}_1 \subseteq S_1 \times S_2\) and \(\mathcal{R}_2 \subseteq S_2 \times S_3\). Then \((\mathcal{R}_2 \circ \mathcal{R}_1)^{-1} = \mathcal{R}_1^{-1} \circ \mathcal{R}_2^{-1}\).