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Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230

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BuyFindarrow_forward

Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
Textbook Problem
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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,bA if ab=ba

(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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