Question:
If $R=\left\{(x, y): x^{2}+y^{2} \leq 4, x, y \in Z\right\}$ is a relation in $\mathrm{Z}$, then the domain of $R$ is
Solution:
Given: $R=\left\{(x, y): x^{2}+y^{2} \leq 4, x, y \in Z\right\}$
$R=\{(-2,0),(2,0),(0,2),(0,-2),(-1,1),(-1,-1),(1,-1),(1,1),(0,1),(1,0),(-1,0),(0,-1),(0,0)\}$
Therefore, Domain of R = {−2, −1, 0, 1, 2}
Hence, if $R=\left\{(x, y): x^{2}+y^{2} \leq 4, x, y \in Z\right\}$ is a relation in $Z$, then the domain of $R$ is $\{\underline{-2}, \underline{-1}, 0,1,2\}$.