JEE Main 2023 (Online) 31st January Evening Shift | Sets and Relations Question 30 | Mathematics

Among the relations

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

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

$\mathrm{S}$ is transitive but $\mathrm{T}$ is not

both $\mathrm{S}$ and $\mathrm{T}$ are symmetric

neither $S$ nor $T$ is transitive

$T$ is symmetric but $S$ is not

JEE Main 2023 (Online) 31st January Morning Shift

MCQ (Single Correct Answer)

-1

Let $$\mathrm{R}$$ be a relation on $$\mathrm{N} \times \mathbb{N}$$ defined by $$(a, b) ~\mathrm{R}~(c, d)$$ if and only if $$a d(b-c)=b c(a-d)$$. Then $$\mathrm{R}$$ is

symmetric and transitive but not reflexive

reflexive and symmetric but not transitive

transitive but neither reflexive nor symmetric

symmetric but neither reflexive nor transitive

JEE Main 2023 (Online) 30th January Morning Shift

MCQ (Single Correct Answer)

-1

The minimum number of elements that must be added to the relation $$ \mathrm{R}=\{(\mathrm{a}, \mathrm{b}),(\mathrm{b}, \mathrm{c})\}$$ on the set $$\{a, b, c\}$$ so that it becomes symmetric and transitive is :