jee-main 2023 Q74

jee-main · India · session1_31jan_shift2 Proof True/False Justification
Among the relations $S = \left\{(a,b) : a, b \in R - \{0\},\ 2 + \frac{a}{b} > 0\right\}$ and $T = \left\{(a,b) : a, b \in R,\ a^2 - b^2 \in Z\right\}$,
(1) $S$ is transitive but $T$ is not
(2) both $S$ and $T$ are symmetric
(3) neither $S$ nor $T$ is transitive
(4) $T$ is symmetric but $S$ is not
Among the relations\\
$S = \left\{(a,b) : a, b \in R - \{0\},\ 2 + \frac{a}{b} > 0\right\}$ and $T = \left\{(a,b) : a, b \in R,\ a^2 - b^2 \in Z\right\}$,\\
(1) $S$ is transitive but $T$ is not\\
(2) both $S$ and $T$ are symmetric\\
(3) neither $S$ nor $T$ is transitive\\
(4) $T$ is symmetric but $S$ is not