Question

A relation R is defined from {2, 3, 4, 5} to {3, 6, 7, 10} by : x R y ⇔ 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}

Answer 1

(d) {2, 3, 4, 5}

The relation R is defined as
$$\begin{gathered} R=\left\{\left(x,y\right):x\in \left\{2,3,4,5\right\},y\in \left\{3,6,7,10\right\}:x\mathrm{is}\mathrm{relatively}\mathrm{prime}\mathrm{to}y\right\} \\ \Rightarrow R=\left\{\left(2,3\right),\left(2,7\right),\left(3,7\right),\left(3,10\right),\left(4,7\right),\left(5,3\right),\left(5,7\right)\right\} \end{gathered}$$

Hence, the domain of R includes all the values of x, i.e. {2, 3, 4, 5}.