Question

Let $R$ be a relation on $N$ defined by $R=\left\{\overline{)\left(x,y\right)}x+2y=8\right\}$. The domain of $R$ is

• A. $\left\{2,4,8\right\}$
• B. $\left\{2,4,6,8\right\}$
• C. $\left\{2,4,6\right\}$
• D. $\left\{1,2,3,4\right\}$

Answer 1

The correct option is C

$\left\{2,4,6\right\}$

Determine the domain of $R$

We have, $R$ , a relation that is defined as $R=\left\{\overline{)\left(x,y\right)}x+2y=8\right\}$ on $N$.

Consider, $x=1,2,3,4,5,6$

For the above values of $x$, we have the values of, $y=\frac{7}{2},3,\frac{5}{2},2,\frac{3}{2},1$. [Since, $x+2y=8$, given]

Since, $R$ is a relation on the natural numbers, $R=\left\{\left(2,3\right),\left(4,2\right),\left(6,1\right)\right\}$ is the required set of relations.

Therefore, the domain of $R$ is $\left\{2,4,6\right\}$.

Hence, option C is the correct answer,