7. A relation R on a set X is called an equivalence relation if it is symmetric, reflexive, and transitive. (a) Show that congruence modulo m (the relation on Z where we write x =m y if m|(x − y)) is an equivalence relation. (b) Show that every partition P of a set X defines an equivalence relation declaring ~ y if x and y are in the same partition element. by

7. A relation R on a set X is called an equivalence relation if it is symmetric, reflexive, and transitive. (a) Show that congruence modulo m (the relation on Z where we write x =m y if m|(x − y)) is an equivalence relation. (b) Show that every partition P of a set X defines an equivalence relation declaring ~ y if x and y are in the same partition element. by

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 3E: a. Let R be the equivalence relation defined on Z in Example 2, and write out the elements of the...

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