Question:
If $R=\left\{(x, y): x, y \in Z, x^{2}+3 y^{2} \leq 8\right\}$ is a relation on the set of integers $Z$, then the domain of $\mathrm{R}^{-1}$ is :
Correct Option: , 2
Solution:
$\mathrm{R}=\left\{(\mathrm{x}, \mathrm{y}): \mathrm{x}, \mathrm{y} \in \mathrm{z}, \mathrm{x}^{2}+3 \mathrm{y}^{2} \leq 8\right\}$
For domain of $\mathrm{R}^{-1}$
Collection of all integral of y's
For $x=0,3 y^{2} \leq 8$
$\Rightarrow \mathrm{y} \in\{-1,0,1\}$
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