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  4. If R= (x , y) |. x , y ∈ Z , x2 + y2 ≤ 4 is a relation in Z , then domain of R is

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Q. If $R=\left\{\left(x , \, y\right) \left|\right. x , \, y \in Z , \, x^{2} + y^{2} \leq 4\right\}$ is a relation in $Z$ , then domain of $R$ is

NTA AbhyasNTA Abhyas 2020

Solution:

$\because $ $R=\left\{\left(x , \, y\right)|x , \, y \in Z , \, x^{2} + y^{2} \leq 4\right\}$
$R=\left\{\left(- 2 , \, 0\right) , \left(- 1 , \, 0\right) , \left(\right. 0 , \, - 1 \left.\right) , \left(- 1 , \, 1\right) , \left(\right. 1 , \, - 1 \left.\right) , \left(0 , \, - 1\right) \left(0 , \, 1\right) , \left(0 , \, 2\right) , \left(0 , - 2\right) , \left(1 , \, 0\right) , \left(\right. 0 , \, 1 \left.\right) , \left(1 , \, 1\right) , \left(\right. - 1 , \, - 1 \left.\right) , \left(2 , \, 0\right) , \left(\right. 0 , \, 0 \left.\right)\right\}$
Hence, Domain of $R=\left\{- 2 , \, - 1 , \, 0 , \, 1 , \, 2\right\}$