# If R = {(x, y) :

Question:

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

Solution:

Given:

R = {(xy) : xy ∈ 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 $(R)=\{-\overline{2},-1,0,1,2\}$