Verified Solution • 2025–26 Session moderate

QJEEM25Ma386c: JEE Main 2025 Mathematics - Class 11 JEEM25Ma386c Solution: Let . The number of relations on , containing and , which are…

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

Step-by-Step Verified Solution

Transitivity

(1,2)∈R,(2,3)∈R⇒(1,3)∈R

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

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

(3,1)(3,1) cannot be taken

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

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

(3) Both not taken

therefore 3 relations are possible.

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