Question:
Find $\mathrm{R}^{-1}$, when
(i) $R=\{(1,2),(1,3),(2,3),(3,2),(4,5)\}$
(ii) $R=\{(x, y): x, y \in N, x+2 y=8\}$.
Solution:
(i) $R=\{(1,2),(1,3),(2,3),(3,2),(4,5)\}$
$\mathrm{R}^{-1}=\{(2,1),(3,1),(3,2),(2,3),(5,4)\}$
(ii) $R=\{(x, y): x, y \in N, x+2 y=8\}$.
$y=\frac{8-x}{2}$
Put $x=2, y=3$
Put $x=4, y=2$
Put $x=6, y=1$
$R=\{(2,3),(4,2),(6,1)\}$
$\mathrm{R}^{-1}=\{(3,2),(2,4),(1,6)\}$