Question

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

Answer 1

$x+2y=8$ , Given $x,y$ are natural numbers , which implies $x,y>0$

If $y=1$ , we get $x=6$

If $y=2$ , we get $x=4$

If $y=3$ , we get $x=2$

For $y\ge 4$ , $x$ wont be a natural number

So the range of $R$ is $\{1,2,3\}$