Home Maths Set Theory and Relations JEE Main 2025 Let A be the set of all functions and be a…
Maths Set Theory and Relations JEE Main 2025 Single Correct MCQ
Published on: August 12, 2026

Let A be the set of all functions and be a relation on such that and . Then R is:

A
Symmetric and transitive but not reflective
B
Symmetric but neither reflective nor transitive
C
Transitive but neither reflexive nor symmetric
D
Reflexive but neither symmetric nor transitive

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Text Solution

Verified by Experts
The correct answer is:
B

For to be reflexive, must be in .
The means and must be true for all .

But always
Therefore, is not reflexive
If , then and

is symmetric
If and , then

Since, and , then is not necessarily equal to .

Therefore, is not transitive.
The relation is symmetric but not reflexive or transitive.

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