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.
Solution:
Given:
R = {(x, y) : x, y ∈ Z, x2 + y2 ≤ 4}
We know:
$(-2)^{2}+0^{2} \leq 4$
$(2)^{2}+0^{2} \leq 4$
$(-1)^{2}+0^{2} \leq 4$
$(1)^{2}+0^{2} \leq 4$
$(-1)^{2}+(1)^{2} \leq 4$
$0^{2}+0^{2} \leq 4$
$(1)^{2}+(1)^{2} \leq 4$
$(-1)^{2}+(-1)^{2} \leq 4$
$\therefore$ Domain $(R)=\{-\overline{2},-1,0,1,2\}$