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Sets and Relations question

2023 · 31 Jan · Shift 2 · Q31

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PYQ Library
JEE Main
Mathematics
Sets and Relations
2023 · 31 Jan · Shift 2 · Q31

Sets and Relations question

2023 · 31 Jan · Shift 2 · Q31

JEE MainMathematicsSets and RelationsMCQ+4 / −1

Among the relations

\mathrm{S}=\left\{(\mathrm{a}, \mathrm{b}): \mathrm{a}, \mathrm{b} \in \mathbb{R}-\{0\}, 2+\frac{\mathrm{a}}{\mathrm{b}}\gt 0\right\}

and

\mathrm{T}=\left\{(\mathrm{a}, \mathrm{b}): \mathrm{a}, \mathrm{b} \in \mathbb{R}, \mathrm{a}^{2}-\mathrm{b}^{2} \in \mathbb{Z}\right\}

,

A
$\mathrm{S}$ is transitive but $\mathrm{T}$ is not
B
both $\mathrm{S}$ and $\mathrm{T}$ are symmetric
C
neither $S$ nor $T$ is transitive
D
$T$ is symmetric but $S$ is not

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