Explanation Given: { 0 , 1 , 2 , 3 , 4 } Formula Used: The given set forms group if the below four conditions are satisfied The set should be closed with respect to the operation The associative property of the operation should hold true for the elements of set The identity element should exists in the operation for all the elements of set For each element in the set has an inverse. Calculation: The set is given as { 0 , 1 , 2 , 3 , 4 } Condition 1: We have ( 0 + 1 ) mod 6 = 1 mod 6 = 1 , which belongs to { 0 , 1 , 2 , 3 , 4 } ( 1 + 2 ) mod 6 = 3 mod 6 = 3 , which belongs to { 0 , 1 , 2 , 3 , 4 } Thus, set { 0 , 1 , 2 , 3 , 4 } is closed with respect to addition modulo 6 Condition 2: [ [ ( 0 + 1 ) mod 6 ] + 3 ] mod 6 = [ [ 1 mod 6 ] + 3 ] mod 6 = [ 1 + 3 ] mod 6 = 4 mod 6 = 4 [ [ 0 + ( 1 + 3 ) mod 6 ] ] mod 6 = [ 0 [ 4 mod 6 ] ] mod 4 = [ 0 + 4 ] mod 4 =

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4th Edition

ISBN: 9781337652445

Author: Richard N. Aufmann, Joanne Lockwood, Richard D. Nation, Daniel K. Clegg

Publisher: Cengage Learning

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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”.

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Chapter 8.3, Problem 14ES

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Determine whether the below set forms a group with respect to the given operation.

" {0,1,2,3,4} ; addition modulo 6 "

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Chapter 8.3, Problem 13ES

Chapter 8.3, Problem 15ES

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Chapter 8 Solutions

WebAssign Printed Access Card for Aufmann/Lockwood/Nation/Clegg's Mathematical Excursions, 4th Edition, Single-Term

Ch. 8.1 - Determine the day of the week on which you were...Ch. 8.1 - Determine the day of the week on which Abraham...Ch. 8.1 - Determine the day of the week on which January 1,...Ch. 8.1 - Determine the day of the week on which Valentines...Ch. 8.1 - Evaluate each expression, where and indicate...Ch. 8.1 - Evaluate each expression, where and indicate...Ch. 8.1 - Evaluate each expression, where and indicate...Ch. 8.1 - Prob. 4ES Ch. 8.1 - Prob. 5ES Ch. 8.1 - Prob. 6ES

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Determine whether the below set forms a group with respect to the given operation. " { 0 , 1 , 2 , 3 , 4 } ; addition modulo 6 "

Solution Summary: The author determines whether the below set forms a group with respect to the given operation. The associative property of the operation should hold true for the elements of set.

Concept explainers

Determine whether the below set forms a group with respect to the given operation.

" {0,1,2,3,4} ; addition modulo 6 "

Want to see the full answer?

Chapter 8 Solutions

Determine whether the below set forms a group with respect to the given operation. " { 0 , 1 , 2 , 3 , 4 } ; addition modulo 6 "

Solution Summary: The author determines whether the below set forms a group with respect to the given operation. The associative property of the operation should hold true for the elements of set.

Concept explainers

Determine whether the below set forms a group with respect to the given operation. " {0,1,2,3,4} ; addition modulo 6 "

Want to see the full answer?

Chapter 8 Solutions

Determine whether the below set forms a group with respect to the given operation.

" {0,1,2,3,4} ; addition modulo 6 "