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 $R ^{-1}$ is :

• A. $\{-2,-1,1,2\}$
• B. $\{-1,0,1\}$
• C. $\{-2,-1,0,1,2\}$
• D. $\{0,1\}$

Answer 1

Answer: (B)

$R =\left\{( x , y ): x , y \in z , x ^{2}+3 y ^{2} \leq 8\right\}$
For domain of $R ^{-1}$

Collection of all integral of y's
For $x=0, \quad 3 y^{2} \leq 8$
$\Rightarrow y \in\{-1,0,1\}$