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.
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 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04260a20-d9b7-4d40-8318-cc78a4c9fab4%2F3af20bfe-765a-41f6-8b2f-2381f4b36618%2Frkzh1wv_processed.png&w=3840&q=75)
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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