Define a relation on Z as follows: For m, n € Z,m~n ⇒ 5|(m - n).(5.1) Prove that is an equivalence relation.(5.2) List 5 elements in the equivalence class [3].(5.3) How many equivalence classes are there? List them.

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Answered: Define a relation on Z as follows: For…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 6E: In Exercises 610, a relation R is defined on the set Z of all integers, In each case, prove that R...

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Define a relation on Z as follows: For m, n € Z, m~n ⇒ 5|(m - n). (5.1) Prove that is an equivalence relation. (5.2) List 5 elements in the equivalence class [3]. (5.3) How many equivalence classes are there? List them.