First you need to establish what a relation on a set is.

Given the set of all ordered pairs taken from , a relation is any subset of this set.

If we can write and say "x is related to y by R".

An equivalence relation is a relation which is:

a) Reflexive: . All elements are related to themselves.

b) Symmetric: . If one element is related by R to another one, then the other one is likewise related to the first.

c) Transitive: .

Examples:

is an equivalence relation trivially.

is not an equivalence because is always false and means it is not the case that .

Recommend you revise your work on relations, then you should be able to get a better handle on how an equivalence relation works.