Exercise 17.5.15. Find x, y € Z12 such that a 0 and y = 0, but x - y = 0.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.2: Mathematical Induction
Problem 10E
Related questions
Question
Please do Exercise 17.5.15 and please show step by step and explain
![Proposition 17.5.12. For any n € N+, we have
Zn = {0, 1, 2,..., n
and 0, 1, 2,.. n I are all distinct.
Exercise 17.5.13. Prove Proposition 17.5.12. It is sufficient to show (a)
0,1,2,..., n − 1 are distinct; and (b) for any integer, the equivalence class
k is one of 0, 1, 2,...,n - 1.
Exercise 17.5.14. Using the definitions of addition, subtraction, and mul-
tiplication given in part (c) of Definition 17.5.11, make tables that show the
results of:
(a) addition modulo 4.
(b) subtraction modulo 5.
(c) multiplication modulo 6.
Exercise 17.5.15. Find r, y € Z12 such that z ‡0 and y ‡ 0, but x· y =
= 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F892e817a-9b32-4eeb-b8fc-5dd7ffde6479%2Fa67f1f51-9e7c-406d-8aba-e2402f014b2e%2Fawb49jg_processed.png&w=3840&q=75)
Transcribed Image Text:Proposition 17.5.12. For any n € N+, we have
Zn = {0, 1, 2,..., n
and 0, 1, 2,.. n I are all distinct.
Exercise 17.5.13. Prove Proposition 17.5.12. It is sufficient to show (a)
0,1,2,..., n − 1 are distinct; and (b) for any integer, the equivalence class
k is one of 0, 1, 2,...,n - 1.
Exercise 17.5.14. Using the definitions of addition, subtraction, and mul-
tiplication given in part (c) of Definition 17.5.11, make tables that show the
results of:
(a) addition modulo 4.
(b) subtraction modulo 5.
(c) multiplication modulo 6.
Exercise 17.5.15. Find r, y € Z12 such that z ‡0 and y ‡ 0, but x· y =
= 0.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Elements Of Modern Algebra](https://www.bartleby.com/isbn_cover_images/9781285463230/9781285463230_smallCoverImage.gif)
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
![Elements Of Modern Algebra](https://www.bartleby.com/isbn_cover_images/9781285463230/9781285463230_smallCoverImage.gif)
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,