Mathematics · Sets and Relations

JEE Main 2025 — 8 April, Evening Shift — Question 30

Given below are two statements : one is labelled as Statement I and the other is labelled as Statement II:

Let $A=\{0,1,2,3,4,5\}$ . Let $R$ be a relation on $A$ defined by $(x, y) \in R$ if and only if $\max \{x, y\} \in\{3,4\}$ . Then among the statements

Statement I: The number of elements in $R$ is 18.

Statement II: The relation $R$ is symmetric but neither reflexive nor transitive.

In the light of the above statements, choose the correct answer from the options given below :

Option A:
Both statement I and statement Il are correct.
Option B:
Statement I is correct and statement Il is incorrect.
Option C:
Statement I is incorrect and statement Il is correct.
Correct
Option D:
Both statements 1 and statements ll are incorrect.

Answer: C

Step-by-step solution

Let's write the pairs $(x, y)$ in $R$

$(0,3),(1,3),(2,3),(3,3),(4,3),(5,3),(3,0),(3,1),(3,2),(3,4),(3,5),(0,4),(1,4),(2,4),(4,4),(5,4),(4,0),(4,1),(4,2),(4,5)$

There are total $20$ pairs

If $(x, y) \in R$ , then $\max (x, y) \in\{3,4\}$

This means, $\max (y, x) \in\{3,4\}$ .

So, $(y, x) \in R$ .

Thus R is symmetric

Since $\max (5,5)=5 \notin\{3,4\},(5,5) \notin R$

Thus R is not reflexive $(3,4) \in R \&(4,2) \in R$ , but $(3,2) \notin R, 2 \notin\{3,4\}$

Thus, R is not transitive

Therefore, only $S_{2}$ is true

Answer key and solution verified before publishing.

Practise Sets and Relations

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.

Solve a similar one free

Exam: JEE Main 2025
Paper: 8 April, Evening Shift
Subject: Mathematics
Chapter: Sets and Relations
Topic: Relations