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Recall the equivalence relation defined on Z by mn whenever m - n is divisible by 3. Let C be the set {[0], [1], [2]} of equivalence classes. Z→ C by g(x) = [x]. a. Find g(1), g(-1), and g(18) b. Write the set {x: g(x) = [0]} as a subset of ZZ. Define g: Z

Recall the equivalence relation defined on Z by mn whenever m - n is divisible by 3. Let C be the set {[0], [1], [2]} of equivalence classes. Z→ C by g(x) = [x]. a. Find g(1), g(-1), and g(18) b. Write the set {x: g(x) = [0]} as a subset of ZZ. Define g: Z

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.3: Subgroups
Problem 23E: 23. Let be the equivalence relation on defined by if and only if there exists an element in ...
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Recall the equivalence relation defined on Z by mn whenever m - n is divisible by 3. Let C be the set {[0], [1], [2]} of equivalence classes. Z→ C by g(x) = [x]. a. Find g(1), g(-1), and g(18) b. Write the set {x: g(x) = [0]} as a subset of Z. Define g: Z
Transcribed Image Text:Recall the equivalence relation defined on Z by mn whenever m - n is divisible by 3. Let C be the set {[0], [1], [2]} of equivalence classes. Z→ C by g(x) = [x]. a. Find g(1), g(-1), and g(18) b. Write the set {x: g(x) = [0]} as a subset of Z. Define g: Z
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