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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?"

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?"

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 8E: Find a subset of Z that is closed under addition but is not subgroup of the additive group Z.
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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?"
Transcribed Image Text: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?"
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