Mathematics · Sets and Relations

JEE Main 2026 — 8 April, Evening Shift — Question 21

Consider the relation R on the set $\{-2, -1, 0, 1, 2\}$ defined by (a, b) $\in \mathbb{R}$ if and only if $1 + ab > 0$ .

Then among the statements:

I. The number of elements in $R$ is $17$

II. R is an equivalence relation.

Option A:
Only I is true
Correct
Option B:
Only II is true
Option C:
Both I and II are true
Option D:
Neither I nor II is true

Answer: A

Step-by-step solution

Reflexive If $(a, a) \in R$ $\Rightarrow 1+\mathrm{a}^{2}>0$ ⇒ It is reflexive relation Symmetric If $1+\mathrm{ab}>0 \Rightarrow 1+\mathrm{ba}>0$ i.e. If $(a, b) \in R$ and $(b, a) \in R$ Therefore it is symmetric relation Transitive $\because(-2,0) \in R \&(0,2) \in R$

But $(-2,2) \notin \mathrm{R}$ Hence it is not transitive ⇒ It is not an equivalence relation. Check Number of elements in R $\because 1+\mathrm{ab}>0$ $\mathrm{a} \& \mathrm{~b}$ each can be filled by 5 ways ∴ total elements $=25$ But out of these $(-2,-1),(-2,2),(-1,2),(1,-2),(2,-2),(2,-1)$ $(-1,1) \&(1,-1)$ are not in relation.

$25-8=17$

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 8 April, Evening Shift
Subject: Mathematics
Chapter: Sets and Relations
Topic: Relations