Question:
A relation $R$ is defined from $\{2,3,4,5\}$ to $\{3,6,7,10\}$ by : $x R y \Leftrightarrow x$ is relatively prime to $y$. Then, domain of $R$ is
(a) {2, 3, 5}
(b) {3, 5}
(c) {2, 3, 4}
(d) {2, 3, 4, 5}
Solution:
(d) {2, 3, 4, 5}
The relation R is defined as
$R=\{(x, y): x \in\{2,3,4,5\}, y \in\{3,6,7,10\}: x$ is relatively prime to $y\}$
$\Rightarrow R=\{(2,3),(2,7),(3,7),(3,10),(4,7),(5,3),(5,7)\}$
Hence, the domain of R includes all the values of x, i.e. {2, 3, 4, 5}.