Maths-

General

Easy

Question

# Which one of the following relations on R is equivalence relation

## The correct answer is:

### To find the equivalence relation from the given options.

An equivalence relation is a relation that is reflexive, symmetric and transitive.

In first option, |x| = |y|

Reflexive: (x, x) ∈ R

x = x

Symmetric: (x, y) ∈ R

(y, x) ∈ R

Transitive: (x, y), (y, z) ∈ R

then (x, z) ∈ R

x = z

xR1y ⇔ |x| = |y|

Hence, option 1 is an equivalence relation.

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