Let Z be the set of integers. Z = (- 3, - 2, - 1, 0, 1, 2, 3 ...} Let R be an equivalence relation defined on set Z as “any two elements a and b of Z belongs to R" if a - b = 3m, me Z" %3D Find a partition of Z.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 27E: Prove Theorem 1.40: If is an equivalence relation on the nonempty set , then the distinct...
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Let Z be the set of integers.
Z = {- 3, - 2, - 1, 0, 1, 2, 3 ..}
%3D
Let R be an equivalence relation defined on set Z as “any two elements a
and b of Z belongs to R" if
а - b %3D Зт, тe Z"
Find a partition of Z.
Transcribed Image Text:Let Z be the set of integers. Z = {- 3, - 2, - 1, 0, 1, 2, 3 ..} %3D Let R be an equivalence relation defined on set Z as “any two elements a and b of Z belongs to R" if а - b %3D Зт, тe Z" Find a partition of Z.
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