Question:
If $R=\left\{(x, y): x, y \in \mathbf{Z}, x^{2}+3 y^{2} \leq 8\right\}$ is a relation on the set of integers $\mathbf{Z}$, then the domain of $R^{-1}$ is :
Correct Option: , 4
Solution:
Since, $R=\left\{(x, y): x, y \in \mathbf{Z}, x^{2}+3 y^{2} \leq 8\right\}$
$\therefore R=\{(1,1),(2,1),(1,-1),(0,1),(1,0)\}$
$\Rightarrow D_{R^{-1}}=\{-1,0,1\}$