Explanation From given table, it is observed that the set of all elements in the given mathematical system are { @ , $ , & , % } under the binary operation ‘ Ο ’. Closure: Let @ , $ ∈ { @ , $ , & , % } . Then, @ − $ is @ which is an element that belongs to the same set. That is, the system does not contain a symbol other than @ , $ , & , % . For any two elements from the system, the closure property under an operation ‘ Ο ’ is satisfied. This shows that the system satisfies the closure property under the operation ‘ Ο ’. Thus, the system is closed under an operation ‘ Ο ’. Identity: To obtain the identity element, check the identical rows and identical columns. The row of elements to the right of $ is identical to the top row and the column of elements under $ is identical to the far-left column. Therefore, $ is the identity element of the system under the operation ‘O’. Inverse: Let a ∈ { @ , $ , & , % } . Then, a O ( − a ) = ( − a ) O a = 0

Survey of Mathematics with Applications with Integrated Review, A, Books a la carte edition, plus MyLab Math Student Access Card and Sticker (10th Edition)

10th Edition

ISBN: 9780134212364

Author: Angel

Publisher: PEARSON

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Chapter 9, Problem 10T

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Whether the mathematical system is a commutative group or not.

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Chapter 9, Problem 9T

Chapter 9, Problem 11T

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Survey of Mathematics with Applications with Integrated Review, A, Books a la carte edition, plus MyLab Math Student Access Card and Sticker (10th Edition)

Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E Ch. 9.1 - Prob. 9E Ch. 9.1 - Prob. 10E

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Whether the mathematical system is a commutative group or not.

Solution Summary: The author explains that the mathematical system holds a commutative group.

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Whether the mathematical system is a commutative group or not.

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