If $R = \{(x, y) : x, y \in \mathbb{Z}, x^2 + y^2 \leq 4\}$ is a relation on the set $\mathbb{Z}$, then domain of $R$ is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\{-2, -1, 0, 1, 2\}$ ##
Given, $R = \{(x, y) : x, y \in \mathbb{Z}, x^2 + y^2 \leq 4\}$
Let $y = 0$, then $x^2 \leq 4 ⇒x = 0, \pm 1, \pm 2$
Thus, the domain of $R = \{-2, -1, 0, 1, 2\}$