JEE PYQ: Sets And Relations Question 5
Question 5 - 2020 (02 Sep Shift 1)
If $R = {(x, y) : x, y \in \mathbf{Z}, x^2 + 3y^2 \leq 8}$ is a relation on the set of integers $\mathbf{Z}$, then the domain of $R^{-1}$ is:
(1) ${-2, -1, 1, 2}$
(2) ${0, 1}$
(3) ${-2, -1, 0, 1, 2}$
(4) ${-1, 0, 1}$
Show Answer
Answer: (4)
Solution
Since $R = {(x, y) : x, y \in \mathbf{Z}, x^2 + 3y^2 \leq 8}$
$\therefore R = {(1, 1), (2, 1), (1, -1), (0, 1), (1, 0)}$ (and symmetric counterparts)
$\Rightarrow D_{R^{-1}} = {-1, 0, 1}$
BETA
