Question

Let R be the relation defined on the set N of rational numbers by the rule xRy if $x+2y=8,$ then domain of R is:

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

Answer 1

Answer: (B)

$\{2,4,6\}$

Given relation between$x$ and $y$ is

$x+2y=8\Rightarrow x=8-2y;x,y\in N$.

When $y=1,x=8-2\times 1=6$

When $y=2,x=8-2\times 2=4$

When $y=3,x=8-2\times 3=2$

For $y>3,x=8-2y\le 0$ and hence x∉N

Hence the relation

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

∴ The domain of the given relation is $2,4,6$