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. (5.3) How many equivalence classes are there
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. (5.3) How many equivalence classes are there
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.
(5.3) How many equivalence classes are there? List them.
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