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QuestionMathsClass 12

If $$R=\left\{ (x,y):{ x }^{ 2 }+{ y }^{ 2 }\le 4;x,y\in \mathbb{Z} \right\}$$ is a relation on $$\mathbb{Z}$$, write the domain of $$R$$.

Given the relation$$R=\left\{ (x,y):{ x }^{ 2 }+{ y }^{ 2 }\le 4;x,y\in \mathbb{Z} \right\}$$.
Since $$a,b$$ are integers then the domain of the relation, i.e. the set of integers satisfying the given equation will be $$R$$ will be$$\left\{ 0,\pm 1,\pm 2 \right\}$$.