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WHAT MEAN BY EQUAELENCE RELATION
An equivalence relation is a relation that, partitions a set so that every element of the set is a member of one and only one cell of the partition. Two elements of the set are considered equivalent (with respect to the equivalence relation) if and only if they are elements of the same cell. The intersection of any two different cells is empty; the union of all the cells equals the original set.

A given binary relation ~ on a set A is said to be an equivalence relation if and only if it is reflexive, symmetric and transitive. Equivalently, for all a, b and c in A:

    a ~ a. (Reflexivity)
    if a ~ b then b ~ a. (Symmetry)
    if a ~ b and b ~ c then a ~ c. (Transitivity)


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