equivalence relation is the relation that holds between two elements if and only if they are members of the same cell within a set that has been partitioned into cells such that every element of the set is a member of one and only one cell of the partition
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A relation between a domain and its codomain is an Equivalence relation if and only if it is reflexive, symmetric and transitive.

A = { (x,y) |   x is a friend of y  }
For example:
D = { a , b, c, d }

A : D --> D
   = { (a, a) , (a, b) , (b, a) , (c, d), (d, c), (b, b), c, c), (d, d) }

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