following table: x 1 2 4 5 7 8 1 1 2 4 5 7 8 2 2 4 8 1 5

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.1: Postulates For The Integers (optional)
Problem 26E: Prove that the cancellation law for multiplication holds in Z. That is, if xy=xz and x0, then y=z.
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Does the Identity law and closure law hold for the following:

1. Addition table for Z9

2. Multiplication table for Z9

3. The following table:

x 1 2 4 5 7 8
1 1 2 4 5 7 8
2 2 4 8 1 5 7
4 4 8 7 2 1 5
5 5 1 2 7 8 4
7 7 5 1 8 4 2
8 8 7 5 4 2 1

 

 

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