a) Explanation Given Information: The set S = { A , B , C } is given and the table that defines the binary operation on the set S is given as: ∗ A B C A A B C B B C A C C A B Explanation: Consider the given table b) To determine Whether there is an identity element in S . c) To determine The inverse of elements of S if there is any identity element.

8th Edition

ISBN: 9780357671139

Author: Gilbert

Publisher: CENGAGE L

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

Question

Chapter 1.4, Problem 4E

To determine

Whether the given binary operation is commutative.

To determine

Whether there is an identity element in S.

To determine

The inverse of elements of S if there is any identity element.

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Chapter 1.4, Problem 3E

Chapter 1.4, Problem 5E

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Chapter 1 Solutions

ELEMENTS OF MODERN ALGEBRA

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Whether the given binary operation is commutative.

Solution Summary: The author explains that the given binary function ast is commutative.

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Whether the given binary operation is commutative.

Whether there is an identity element in S.

The inverse of elements of S if there is any identity element.

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Chapter 1 Solutions