Prove or disprove that H = {nEZ\n is divisible by both 8 and 10}is a subgroup of Z. What happens if “divisible by both 8 and 10" ischanged to "divisible by 8 or 10?"

Given: H=n∈Z n is divisible by both 8 and 10We need to show whether H is a subgroup of Z or not and…

Answered: Prove or disprove that H = {nEZ\n is…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.3: Permutation Groups In Science And Art (optional)

Problem 17E

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Prove or disprove that H = {nEZ\n is divisible by both 8 and 10} is a subgroup of Z. What happens if “divisible by both 8 and 10" is changed to "divisible by 8 or 10?"