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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 $x=6, y=1$

$R=\{(2,3),(4,2),(6,1)\}$

$\mathrm{R}^{-1}=\{(3,2),(2,4),(1,6)\}$