Given $A=\left\{1,2,3\right\}$, $B=\left\{3,4,5,6\right\}$ and $C=\left\{6,7,8,9\right\}$
A Relation $R \subset A \times B$ such that $xRy$ iff $4x \lt y$ and a Relation $S$ is defined as
$S \subset B \times C$ such that $ySz$ iff $2y \le z$ We have to find $S^{-1}oR$
we get $$R=\left\{(1,5),(1,6)\right\}$$
and $$S=\left\{(3,6),(3,7),(3,8),(3,9),(4,8),(4,9)\right\}$$
hence $$S^{-1} \subset C \times B$$ is given by
$$S^{-1}=\left\{(6,3),(7,3),(8,3),(9,3),(8,4),(9,4)\right\}$$
Now my book gave answer as $$S^{-1}\circ R=\left\{(1,3)\right\}$$
But is $S^{-1}\circ R$ defined here?