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If \(\displaystyle R=\{ (x,y):x, y \in Z ,x^{2}+y^{2}\leq 4 \}\) is a relation in \(Z\) then domain \(D\) is

(A) \(\displaystyle \left \{ -2,-1,0,1,2\right \}\)
(B) \(\displaystyle \left \{ -2,-1,0 \right \}\)
(C) \(\displaystyle \left \{ 0,1,2\right \}\)
(D) None of these

Answer

Answer: A
Relation \(Z\) consists of all the integral points inside and onthe circle of radius \(2\) and center \((0,0)\).

For all the points \((x,y)\) which lie inside and on the circle \(x\epsilon [-2,2]\) and \(y\epsilon [-2,2]\). Hence the domain is the integer values of \(x\) i.e \(-2,-1,0,1,2.\)

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