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 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.
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