Question

If R = \{x, y : x, y \epsilon Z, x^2 + y^2 \leq 4\} is a relation defined on the set Z of integers, then write domain of R.

Answer 1

We have,

$R=\{x,y:x,yϵZ,x^2+y^2\le 4\}$

Now,

$x^2+y^2\le 4$

$\Rightarrow y^2\le 4-x^2$

$\Rightarrow y\le \sqrt{4-x^2}$

Putting x = - 2, -1, 0, 1, 2, we get $yϵz.$

For other values of x, we get $y\text{/}ϵz.$

$\therefore$ Domain (R) = {-2, -1, 0, 1, 2}