Explore BrainMass

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.

The fully formatted problem is in the attached file.


Solution Preview

The solution of the Posting is in the attached file.

Thanks for using BrainMass.com. Have a great day.

Modern Algebra
Set Theory (I)

Solution Summary

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