Q. If $R=\left\{(x, y): x, y \in Z, x^2+y^2 \leq 4\right\}$ is a relation, then domain of $R$ is
Relations and Functions
Solution:
Given, $R=\left\{(x, y): x, y \in Z, x^2+y^2 \leq 4\right\}$
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 $x^2+y^2 \leq a^2$. Hence, we can also take interior integral points.
