Question

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

• A. $\{0,1,2\}$
• B. $\{0,-1,-2\}$
• C. $\{-2,-1,0,1,2\}$
• D. None of these

Answer 1

Answer: (C)

Given, $R=\left\{(x,y):x,y\in Z,x^2+y^2\le 4\right\}$
In Roster form, $R=\{(-2,0),(-1,-1),(-1,1),(-1,0),(0,-2),(0,-1),(0,0)$, $(0,1),(0,2),(1,1),(1,0),(1,-1),(2,0)\}$
Hence, domain of $R=\{-2,-1,0,1,2\}$
Graphically
$x^2+y^2=a^2$ represent circle here. Equation of circle is $x^2+y^2\le a^2$. Hence, we can also take interior integral points.