Home Maths Set Theory and Relations Relations Let be a relation over the set and it is d…
Maths Set Theory and Relations Relations Single Correct MCQ
Published on: August 13, 2026

Let be a relation over the set and it is defined by . Then is

A
Reflexive only
B
Symmetric only
C
Transitive only
D
An equivalence relation

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Text Solution

Verified by Experts
The correct answer is:
D

We have for all

Since . Hence, is reflexive.
is symmetric for we have

Then by definition of , we have and , whence by addition, we get

Hence,
Thus, and .

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