JEE Main 2022 · 28 Jun · Shift 2 · Mathematics Q1

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MathematicsSingle correct+4 / -1Question 1 of 90

Let $R_1=\{(a,b)\in\mathbf N\times\mathbf N:|a-b|\le13\}$ and $R_2=\{(a,b)\in\mathbf N\times\mathbf N:|a-b|\ne13\}$ . Then on $\mathbf N$ :

Both

R_1

and

R_2

are equivalence relations

Neither

R_1

nor

R_2

is an equivalence relation

R_1

is an equivalence relation but

R_2

is not

R_2

is an equivalence relation but

R_1

is not

Answer and worked solution

Official answer: B

Both are reflexive and symmetric. Neither is transitive: for $R_1$ , $(1,14)$ and $(14,27)$ are in but $(1,27)$ is not; for $R_2$ , $(1,2)$ and $(2,14)$ are in but $(1,14)$ is not.

(B)

Topics:Relations

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JEE Main 2022 · 28 Jun · Shift 2, Mathematics question 1