Question

If $R=\left\{\right(x,y):x+2y=8\}$ is a relation on $N$, then write the range of $R$.

Answer 1

Given,

$x+2y=8$

or, $y=\frac{8-x}{2}$

or, $y=4-\frac{x}{2}$

Since the relation is on $N$, so $x$ and $y$ are both natural .

Thus values possible for $x$ are $2,4,6$.

Which gives possible values of y to be $3,2,1$.

Thus Range of $R$ is $\{1,2,3\}$.