Among the relations S = { (a, b): a, b ∈ ℝ \ { 0 }, 2 + a/b > 0 }… | JEE Main 2023 Mathematics PYQ

MCQEasyJEE Main 2023 · 31 January, Shift 2Relations

Among the relations $S = \left\{ (a, b) : a, b \in \mathbb{R} \setminus \{ 0 \}, 2 + \frac{a}{b} > 0 \right\}$ And $T = \left\{ (a, b) : a, b \in \mathbb{R}, a^2 - b^2 \in \mathbb{Z} \right\}$ which of the following is true?

A
$S$ is transitive but $T$ is not.
B
$T$ is symmetric but $S$ is not.
C
Neither $S$ nor $T$ is transitive.
D
Both $S$ and $T$ are symmetric.

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