Question

If R = {(x, y) : x, y ∈ Z, x² + y² ≤ 4} is a relation defined on the set Z of integers, then write domain of R.

Answer 1

Given:
R = {(x, y) : x, y ∈ Z, x² + y² ≤ 4}
We know:
$$\begin{gathered} {\left(-2\right)}^2+0^2\le 4 \\ {\left(2\right)}^2+0^2\le 4 \\ {\left(-1\right)}^2+0^2\le 4 \\ {\left(1\right)}^2+0^2\le 4 \\ {\left(-1\right)}^2+{\left(1\right)}^2\le 4 \\ {0}^2+0^2\le 4 \\ {\left(1\right)}^2+{\left(1\right)}^2\le 4 \\ {\left(-1\right)}^2+{\left(-1\right)}^2\le 4 \end{gathered}$$
∴ Domain (R) = {$-$2, $-$1, 0, 1, 2}