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Math
AlgebraElements Of Modern Algebra8th Edition

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Chapter 1.4, Problem 5E
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Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230

Solutions

Chapter
Section
Problem 1TFE
Problem 2TFE
Problem 3TFE
Problem 4TFE
Problem 5TFE
Problem 6TFE
Problem 7TFE
Problem 8TFE
Problem 9TFE
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
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Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
Textbook Problem
1 views

Let S be the set of four elements given by S = { A , B , C , D }

with the following table.

∗ A B C D
A B C A B
B C D B A
C A B C D
D A B D D

a. Is the binary operation ∗ commutative? Why?

b. Determine whether there is an identity element in S for ∗ .

c. If there is an identity element, which elements have inverses?

(a)

To determine

Whether the binary operation ∗ is commutative on the set S={A,B,C,D}.

Explanation

Given Information: The set S={A,B,C,D} is given and the table that defines the binary operation on the set S is given as:

∗ A B C D
A B C A B
B C D B A
C A B C D
D A B D D

Formula Used:

A binary operation ∗ is said to be commutative for any elements a,b∈A if a∗b=b∗a

(b)

To determine

Whether there is an identity element in S.

(c)

To determine

Whether there is an inverse element of S.

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Sect-1.1 P-1TFESect-1.1 P-2TFESect-1.1 P-3TFESect-1.1 P-4TFESect-1.1 P-5TFESect-1.1 P-6TFESect-1.1 P-7TFESect-1.1 P-8TFESect-1.1 P-9TFESect-1.1 P-10TFE
Sect-1.1 P-1ESect-1.1 P-2ESect-1.1 P-3ESect-1.1 P-4ESect-1.1 P-5ESect-1.1 P-6ESect-1.1 P-7ESect-1.1 P-8ESect-1.1 P-9ESect-1.1 P-10ESect-1.1 P-11ESect-1.1 P-12ESect-1.1 P-13ESect-1.1 P-14ESect-1.1 P-15ESect-1.1 P-16ESect-1.1 P-17ESect-1.1 P-18ESect-1.1 P-19ESect-1.1 P-20ESect-1.1 P-21ESect-1.1 P-22ESect-1.1 P-23ESect-1.1 P-24ESect-1.1 P-25ESect-1.1 P-26ESect-1.1 P-27ESect-1.1 P-28ESect-1.1 P-29ESect-1.1 P-30ESect-1.1 P-31ESect-1.1 P-32ESect-1.1 P-33ESect-1.1 P-34ESect-1.1 P-35ESect-1.1 P-36ESect-1.1 P-37ESect-1.1 P-38ESect-1.1 P-39ESect-1.1 P-40ESect-1.1 P-41ESect-1.1 P-42ESect-1.1 P-43ESect-1.2 P-1TFESect-1.2 P-2TFESect-1.2 P-3TFESect-1.2 P-4TFESect-1.2 P-5TFESect-1.2 P-6TFESect-1.2 P-7TFESect-1.2 P-8TFESect-1.2 P-9TFESect-1.2 P-1ESect-1.2 P-2ESect-1.2 P-3ESect-1.2 P-4ESect-1.2 P-5ESect-1.2 P-6ESect-1.2 P-7ESect-1.2 P-8ESect-1.2 P-9ESect-1.2 P-10ESect-1.2 P-11ESect-1.2 P-12ESect-1.2 P-13ESect-1.2 P-14ESect-1.2 P-15ESect-1.2 P-16ESect-1.2 P-17ESect-1.2 P-18ESect-1.2 P-19ESect-1.2 P-20ESect-1.2 P-21ESect-1.2 P-22ESect-1.2 P-23ESect-1.2 P-24ESect-1.2 P-25ESect-1.2 P-26ESect-1.2 P-27ESect-1.2 P-28ESect-1.3 P-1TFESect-1.3 P-2TFESect-1.3 P-3TFESect-1.3 P-4TFESect-1.3 P-5TFESect-1.3 P-6TFESect-1.3 P-1ESect-1.3 P-2ESect-1.3 P-3ESect-1.3 P-4ESect-1.3 P-5ESect-1.3 P-6ESect-1.3 P-7ESect-1.3 P-8ESect-1.3 P-9ESect-1.3 P-10ESect-1.3 P-11ESect-1.3 P-12ESect-1.4 P-1TFESect-1.4 P-2TFESect-1.4 P-3TFESect-1.4 P-4TFESect-1.4 P-5TFESect-1.4 P-6TFESect-1.4 P-7TFESect-1.4 P-8TFESect-1.4 P-9TFESect-1.4 P-1ESect-1.4 P-2ESect-1.4 P-3ESect-1.4 P-4ESect-1.4 P-5ESect-1.4 P-6ESect-1.4 P-7ESect-1.4 P-8ESect-1.4 P-9ESect-1.4 P-10ESect-1.4 P-11ESect-1.4 P-12ESect-1.4 P-13ESect-1.4 P-14ESect-1.4 P-15ESect-1.4 P-16ESect-1.5 P-1TFESect-1.5 P-2TFESect-1.5 P-3TFESect-1.5 P-1ESect-1.5 P-2ESect-1.5 P-3ESect-1.5 P-4ESect-1.5 P-5ESect-1.5 P-6ESect-1.5 P-7ESect-1.5 P-8ESect-1.5 P-9ESect-1.5 P-10ESect-1.6 P-1TFESect-1.6 P-2TFESect-1.6 P-3TFESect-1.6 P-4TFESect-1.6 P-5TFESect-1.6 P-6TFESect-1.6 P-7TFESect-1.6 P-8TFESect-1.6 P-9TFESect-1.6 P-10TFESect-1.6 P-11TFESect-1.6 P-12TFESect-1.6 P-1ESect-1.6 P-2ESect-1.6 P-3ESect-1.6 P-4ESect-1.6 P-5ESect-1.6 P-6ESect-1.6 P-7ESect-1.6 P-8ESect-1.6 P-9ESect-1.6 P-10ESect-1.6 P-11ESect-1.6 P-12ESect-1.6 P-13ESect-1.6 P-14ESect-1.6 P-15ESect-1.6 P-16ESect-1.6 P-17ESect-1.6 P-18ESect-1.6 P-19ESect-1.6 P-20ESect-1.6 P-21ESect-1.6 P-22ESect-1.6 P-23ESect-1.6 P-24ESect-1.6 P-25ESect-1.6 P-26ESect-1.6 P-27ESect-1.6 P-28ESect-1.6 P-29ESect-1.6 P-30ESect-1.6 P-31ESect-1.6 P-32ESect-1.7 P-1TFESect-1.7 P-2TFESect-1.7 P-3TFESect-1.7 P-4TFESect-1.7 P-5TFESect-1.7 P-6TFESect-1.7 P-1ESect-1.7 P-2ESect-1.7 P-3ESect-1.7 P-4ESect-1.7 P-5ESect-1.7 P-6ESect-1.7 P-7ESect-1.7 P-8ESect-1.7 P-9ESect-1.7 P-10ESect-1.7 P-11ESect-1.7 P-12ESect-1.7 P-13ESect-1.7 P-14ESect-1.7 P-15ESect-1.7 P-16ESect-1.7 P-17ESect-1.7 P-18ESect-1.7 P-19ESect-1.7 P-20ESect-1.7 P-21ESect-1.7 P-22ESect-1.7 P-23ESect-1.7 P-24ESect-1.7 P-25ESect-1.7 P-26ESect-1.7 P-27ESect-1.7 P-28ESect-1.7 P-29ESect-1.7 P-30E

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