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Set Theory - Equivalence Relation

Modern Algebra
Set Theory (I)
Equivalence Relation

Let S be the set of all integers and let n > 1 be a fixed integer.
Define for a,b in S, a ~ b if a - b is a multiple of n.
Prove that this defines an equivalence relation on S.

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Modern Algebra
Set Theory (I)

Solution Summary

An equivalence relation is defined in this problem. The solution is detailed and well presented.