Mathematics · Sets and Relations

JEE Main 2025 — 22 January, Evening Shift — Question 25

Let $\mathrm{A}=\{1,2,3\}$ . The number of relations on A , containing $( 1,2 )$ and $(2,3)$ , which are reflexive and transitive but not symmetric, is $\_\_\_\_\_$ .

Answer: 3

Numerical answer — enter this value.

Step-by-step solution

Transitivity

$(1,2) \in \mathrm{R},(2,3) \in \mathrm{R} \Rightarrow(1,3) \in \mathrm{R}$

For reflexive $(1,1),(2,2)(3,3) \in R$

Now (2, 1), $(3,2),(3,1)$

$(3,1)$ cannot be taken

(1) $(2,1)$ taken and $(3,2)$ not taken

(2) $(3,2)$ taken and $(2,1)$ not taken

(3) Both not taken

therefore 3 relations are possible.

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 22 January, Evening Shift
Subject: Mathematics
Chapter: Sets and Relations
Topic: Relations