# R is a relation from {11, 12, 13} to {8, 10, 12} defined by

Question:

$R$ is a relation from $\{11,12,13\}$ to $\{8,10,12\}$ defined by $y=x-3$. Then, $R^{-1}$ is

(a) {(8, 11), (10, 13)}
(b) {(11, 8), (13, 10)}
(c) {(10, 13), (8, 11)}
(d) none of these

Solution:

(a) {(8, 11), (10, 13)}

The relation R is defined by

$R=\{(x, y): x \in\{11,12,13\}, y \in\{8,10,12\}: y=x-3\}$

$\Rightarrow R=\{(11,8),(13,10)\}$

So, $R^{-1}=\{(8,11),(10,13)\}$