# A relation R is defined from

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}.