How do you solve c)? Recall thatZ, = {[0), [1], [2], . .. [n – 1]}is the set of congruence classes (or equivalence classes) modulo n. For instance, Z, = {[0], [1], [2], [3), [4)}are the congruence classes modulo 5.(a) Show that the collection{{2i] : 0

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Description: How do you solve c)? Recall thatZ, = {[0), [1], [2], . .. [n – 1]}is the set of congruence classes (or equivalence classes) modulo n. For instance, Z, = {[0], [1], [2], [3), [4)}are the congruence classes modulo 5.(a) Show that the collection{{2i] :

Answered: (c) Show that the collection {{2i] : 0…

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(c) Show that the collection {{2i] : 0 < i < n – 1} is a partition of the integers into n disjoint congruence classes modulo n if and only if n is odd.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.5: Normal Subgroups

Problem 31E

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