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.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 28E
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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.
Transcribed Image Text: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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