Consider the set Z₁0 under multiplication. [0] does not have a multiplicative inverse. So, Z10 is not a group under multiplication. Is Z₁0 - {[0]} a group under multiplication? (Hint: Think about the inverse axiom for a group.)
Consider the set Z₁0 under multiplication. [0] does not have a multiplicative inverse. So, Z10 is not a group under multiplication. Is Z₁0 - {[0]} a group under multiplication? (Hint: Think about the inverse axiom for a group.)
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.1: Definition Of A Group
Problem 45E: 45. Let . Prove or disprove that is a group with respect to the operation of intersection. (Sec. )
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![Consider the set Z₁0 under multiplication. [0] does not have a multiplicative inverse. So,
Z10 is not a group under multiplication. Is Z₁0 - {[0]} a group under multiplication?
(Hint: Think about the inverse axiom for a group.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F545e4110-447f-42e0-86d8-f710095b2322%2F2f7563e9-822d-4e08-a691-e6ede12ddf50%2Fcx6ids_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the set Z₁0 under multiplication. [0] does not have a multiplicative inverse. So,
Z10 is not a group under multiplication. Is Z₁0 - {[0]} a group under multiplication?
(Hint: Think about the inverse axiom for a group.)
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