Question

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

Answer 1

R=$\left\{(x,y):x+2y=8\right\},x,yϵN$

$x+2y=8\Rightarrow x=8-2y=2(4-y)$

$\therefore x$ is a multiple of 2, hence an even number.

Values of x can be 2, 4, 6....
when $x=2,2y=6\Rightarrow y=3$

when $x=4,2y=4\Rightarrow y=2$

when $x=6,2y=2\Rightarrow y=1$
If we put x more than 6, the value of y will not be a natural number.

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

Range of R={1,2,3}