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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Question
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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