Question

If $R=\left\{\right(x,y)|x,y\in Z,x^2+y^2\le 4\}$ is a relation in $Z$, then domain of $R$ is

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

Answer 1

The correct option is C $\{-2,-1,0,1,2\}$

As $R=\left\{\right(x,y)|x,y\in Z,x^2+y^2\le 4\}$

If $y=0\Rightarrow x=0,\pm 1,\pm 2$
If $y=\pm 1\Rightarrow x=0,\pm 1$
If $y=\pm 2\Rightarrow x=0$
$\therefore \text{domain of}R=\{-2,-1,0,1,2\}$