Chapter 3.1, Problem 18E

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8th Edition

Gilbert + 2 others

ISBN: 9781285463230

Textbook Problem

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In Exercises

To determine

Whether

Explanation

**Given information:**

The binary operation

**Explanation:**

Suppose the binary operation

1.

2.

3.

4.

Condition for an abelian group:

First check if

First condition:

Let

Therefore, the set

Second condition:

Let

As

Sect-3.1 P-1TFESect-3.1 P-2TFESect-3.1 P-3TFESect-3.1 P-4TFESect-3.1 P-5TFESect-3.1 P-6TFESect-3.1 P-7TFESect-3.1 P-8TFESect-3.1 P-9TFESect-3.1 P-10TFE

Sect-3.1 P-11TFESect-3.1 P-1ESect-3.1 P-2ESect-3.1 P-3ESect-3.1 P-4ESect-3.1 P-5ESect-3.1 P-6ESect-3.1 P-7ESect-3.1 P-8ESect-3.1 P-9ESect-3.1 P-10ESect-3.1 P-11ESect-3.1 P-12ESect-3.1 P-13ESect-3.1 P-14ESect-3.1 P-15ESect-3.1 P-16ESect-3.1 P-17ESect-3.1 P-18ESect-3.1 P-19ESect-3.1 P-20ESect-3.1 P-21ESect-3.1 P-22ESect-3.1 P-23ESect-3.1 P-24ESect-3.1 P-25ESect-3.1 P-26ESect-3.1 P-27ESect-3.1 P-28ESect-3.1 P-29ESect-3.1 P-30ESect-3.1 P-31ESect-3.1 P-32ESect-3.1 P-33ESect-3.1 P-34ESect-3.1 P-35ESect-3.1 P-36ESect-3.1 P-37ESect-3.1 P-38ESect-3.1 P-39ESect-3.1 P-40ESect-3.1 P-41ESect-3.1 P-42ESect-3.1 P-43ESect-3.1 P-44ESect-3.1 P-45ESect-3.1 P-46ESect-3.1 P-47ESect-3.1 P-48ESect-3.1 P-49ESect-3.1 P-50ESect-3.1 P-51ESect-3.1 P-52ESect-3.2 P-1TFESect-3.2 P-2TFESect-3.2 P-3TFESect-3.2 P-4TFESect-3.2 P-5TFESect-3.2 P-6TFESect-3.2 P-1ESect-3.2 P-2ESect-3.2 P-3ESect-3.2 P-4ESect-3.2 P-5ESect-3.2 P-6ESect-3.2 P-7ESect-3.2 P-8ESect-3.2 P-9ESect-3.2 P-10ESect-3.2 P-11ESect-3.2 P-12ESect-3.2 P-13ESect-3.2 P-14ESect-3.2 P-15ESect-3.2 P-16ESect-3.2 P-17ESect-3.2 P-18ESect-3.2 P-19ESect-3.2 P-20ESect-3.2 P-21ESect-3.2 P-22ESect-3.2 P-23ESect-3.2 P-24ESect-3.2 P-25ESect-3.2 P-26ESect-3.2 P-27ESect-3.2 P-28ESect-3.2 P-29ESect-3.2 P-30ESect-3.2 P-31ESect-3.2 P-32ESect-3.3 P-1TFESect-3.3 P-2TFESect-3.3 P-3TFESect-3.3 P-4TFESect-3.3 P-5TFESect-3.3 P-6TFESect-3.3 P-7TFESect-3.3 P-8TFESect-3.3 P-9TFESect-3.3 P-10TFESect-3.3 P-11TFESect-3.3 P-1ESect-3.3 P-2ESect-3.3 P-3ESect-3.3 P-4ESect-3.3 P-5ESect-3.3 P-6ESect-3.3 P-7ESect-3.3 P-8ESect-3.3 P-9ESect-3.3 P-10ESect-3.3 P-11ESect-3.3 P-12ESect-3.3 P-13ESect-3.3 P-14ESect-3.3 P-15ESect-3.3 P-16ESect-3.3 P-17ESect-3.3 P-18ESect-3.3 P-19ESect-3.3 P-20ESect-3.3 P-21ESect-3.3 P-22ESect-3.3 P-23ESect-3.3 P-24ESect-3.3 P-25ESect-3.3 P-26ESect-3.3 P-27ESect-3.3 P-28ESect-3.3 P-29ESect-3.3 P-30ESect-3.3 P-31ESect-3.3 P-32ESect-3.3 P-33ESect-3.3 P-34ESect-3.3 P-35ESect-3.3 P-36ESect-3.3 P-37ESect-3.3 P-38ESect-3.3 P-39ESect-3.3 P-40ESect-3.3 P-41ESect-3.3 P-42ESect-3.3 P-43ESect-3.3 P-44ESect-3.3 P-45ESect-3.4 P-1TFESect-3.4 P-2TFESect-3.4 P-3TFESect-3.4 P-4TFESect-3.4 P-5TFESect-3.4 P-6TFESect-3.4 P-7TFESect-3.4 P-8TFESect-3.4 P-9TFESect-3.4 P-10TFESect-3.4 P-1ESect-3.4 P-2ESect-3.4 P-3ESect-3.4 P-4ESect-3.4 P-5ESect-3.4 P-6ESect-3.4 P-7ESect-3.4 P-8ESect-3.4 P-9ESect-3.4 P-10ESect-3.4 P-11ESect-3.4 P-12ESect-3.4 P-13ESect-3.4 P-14ESect-3.4 P-15ESect-3.4 P-16ESect-3.4 P-17ESect-3.4 P-18ESect-3.4 P-19ESect-3.4 P-20ESect-3.4 P-21ESect-3.4 P-22ESect-3.4 P-23ESect-3.4 P-24ESect-3.4 P-25ESect-3.4 P-26ESect-3.4 P-27ESect-3.4 P-28ESect-3.4 P-29ESect-3.4 P-30ESect-3.4 P-31ESect-3.4 P-32ESect-3.4 P-33ESect-3.4 P-34ESect-3.4 P-35ESect-3.4 P-36ESect-3.4 P-37ESect-3.4 P-38ESect-3.4 P-39ESect-3.4 P-40ESect-3.4 P-41ESect-3.4 P-42ESect-3.5 P-1TFESect-3.5 P-2TFESect-3.5 P-3TFESect-3.5 P-4TFESect-3.5 P-5TFESect-3.5 P-6TFESect-3.5 P-7TFESect-3.5 P-8TFESect-3.5 P-1ESect-3.5 P-2ESect-3.5 P-3ESect-3.5 P-4ESect-3.5 P-5ESect-3.5 P-6ESect-3.5 P-7ESect-3.5 P-8ESect-3.5 P-9ESect-3.5 P-10ESect-3.5 P-11ESect-3.5 P-12ESect-3.5 P-13ESect-3.5 P-14ESect-3.5 P-15ESect-3.5 P-16ESect-3.5 P-17ESect-3.5 P-18ESect-3.5 P-19ESect-3.5 P-20ESect-3.5 P-21ESect-3.5 P-22ESect-3.5 P-23ESect-3.5 P-24ESect-3.5 P-25ESect-3.5 P-26ESect-3.5 P-27ESect-3.5 P-28ESect-3.5 P-29ESect-3.5 P-30ESect-3.5 P-31ESect-3.5 P-32ESect-3.5 P-33ESect-3.5 P-34ESect-3.5 P-35ESect-3.5 P-36ESect-3.5 P-37ESect-3.5 P-38ESect-3.5 P-39ESect-3.6 P-1TFESect-3.6 P-2TFESect-3.6 P-3TFESect-3.6 P-4TFESect-3.6 P-5TFESect-3.6 P-6TFESect-3.6 P-7TFESect-3.6 P-8TFESect-3.6 P-9TFESect-3.6 P-10TFESect-3.6 P-1ESect-3.6 P-2ESect-3.6 P-3ESect-3.6 P-4ESect-3.6 P-5ESect-3.6 P-6ESect-3.6 P-7ESect-3.6 P-8ESect-3.6 P-9ESect-3.6 P-10ESect-3.6 P-11ESect-3.6 P-12ESect-3.6 P-13ESect-3.6 P-14ESect-3.6 P-15ESect-3.6 P-16ESect-3.6 P-17ESect-3.6 P-18ESect-3.6 P-19ESect-3.6 P-20ESect-3.6 P-21ESect-3.6 P-22ESect-3.6 P-23ESect-3.6 P-24ESect-3.6 P-25E

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