Let $R_1$ and $R_2$ be two relations defined on $\mathbb{R}$ by $a\,R_1\,b \Leftrightarrow ab \ge 0$ and $a\,R_2\,b \Leftrightarrow a \ge b$ Then,

Option 4: neither $R_1$ nor $R_2$ is an equivalence relation

$R_1$ is an equivalence relation but not $R_2$

$R_2$ is an equivalence relation but not $R_1$

both $R_1$ and $R_2$ are equivalence relations

neither $R_1$ nor $R_2$ is an equivalence relation

JEE Main 2022 · MathsMultiple choiceSingle correctEasyConceptual

JEE Main 27 July 2022, Shift 1, Maths Q1

Question 1 of 90 in this shift, Maths question 1 of 30, Section A.

Let

R_1

and

R_2

be two relations defined on

\mathbb{R}

a\,R_1\,b \Leftrightarrow ab \ge 0

and

a\,R_2\,b \Leftrightarrow a \ge b

Then,

(1) $R_1$ is an equivalence relation but not $R_2$
(2) $R_2$ is an equivalence relation but not $R_1$
(3)both $R_1$ and $R_2$ are equivalence relations
(4)neither $R_1$ nor $R_2$ is an equivalence relationOfficial answer

Official answer

Option 4

NTA final key.

Chapter: Relations and Functions
Topic: Sets and Relations
Idea tested: Equivalence Relations

Same idea in other shifts

Asked 10× in all

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.