Question

Let A={2,3,6,12}and let R and S be the following relations on A. xRyiff 2 / x–y, xSyiff 3 / x–y. Compute the following R^---,R^S,R U S,S^-1

Answer 1

$A=\{2,3,6,12\}\\ xRy \ iff \ 2|x-y\\ R=\{(2,3),(3,2)\}\\ xSy \ iff \ 3|x-y\\ S=\{(2,3),(3,2),(3,6),(6,3)\}\\ R^{-1}=\{(3,2),(2,3)\}\\ R\cap S=\{(2,3),(3,2)\}\\ R\cup S=\{(2,3),(3,2),(3,6),(6,3)\}\\ S^{-1}=\{(3,2),(2,3),(6,3),(3,6)\}$