Question

Let $R$ be a relation on $N$ defined by $x+2y=8$. The domain of $R$ is

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

Answer 1

The correct option is D $\{2,4,6\}$

Given: $x+2y=8$

$\Rightarrow x=8-2y$

We know relation is defined on $N$, so

$x\ge 1$

$\Rightarrow 8-2y\ge 1$

$\Rightarrow y\le \frac{7}{2}$

Also, $y\in N$, so

$y=1,2,3$

$\Rightarrow 2y=2,4,6$

$\Rightarrow -2y=-2,-4,-6$

$\Rightarrow x=8-2y=6,4,2$

$R=\left\{\right(2,3),(4,2),(6,1\left)\right\}$

$\therefore$ Domain of $R=\{2,4,6\}$

Therefore, the correct option is $\left(C\right)$