In mathematics, an equivalence relation is denoted by **R** or **$\sim$** or **$\equiv$**. A relation is said to be an equivalence relation **if and only if** it is -

- Reflexive
- Symmetric
- Transitive

Let us study each in detail.

a R a, $\forall$ a $\epsilon$ S

Equality over a set real numbers is a reflexive relation.if a R b $\Rightarrow$ b R a $\forall$ a, b $\epsilon$ S

a = b is a symmetric relation, since a = b $\Rightarrow$ b = a, where a and b are real numbers.if a R b and b R c $\Rightarrow$ a R c $\forall$ a, b, c $\epsilon$ S

Where, R is a symmetric relation defined over the set S. Equality is also a transitive relation.Since the relation "

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