Explanation Given: Set { 1 , 2 , 3 , 4 } Calculation: Set { 1 , 2 , 3 , 4 } with the multiplication operation mod 5 is closed. 2 ⋅ 1 mod 5 ≡ 2 mod 5 ≡ 2 2 ⋅ 3 mod 5 ≡ 6 mod 5 ≡ 1 Set { 1 , 2 , 3 , 4 } is true for the associative property. [ ( 2 ⋅ 1 mod 5 ) ⋅ 3 ] mod 5 = [ ( 2 mod 5 ) ⋅ 3 ] mod 5 = 2 ⋅ 3 mod 5 ≡ 6

Mathematical Excursions (MindTap Course List)

4th Edition

ISBN: 9781305965584

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

Publisher: Cengage Learning

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Chapter 8, Problem 16T

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Whether the given set with the multiplication operation modulo 5 forms a group.

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Chapter 8, Problem 15T

Chapter 8, Problem 17T

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Mathematical Excursions (MindTap Course List)

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Whether the given set with the multiplication operation modulo 5 forms a group.

Solution Summary: The author determines whether the given set with the multiplication operation modulo 5 forms a group. Each element in the set has multiplicative inverse.

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Whether the given set with the multiplication operation modulo 5 forms a group.

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