2 Let Z be the set of integers and let m be a fixed positive integer. Define the relation by y if and only if m divides a- y (equivalently ay is a multiple of m). This is called the relation congruence modulo m in Z. (a) Prove that this relation is an equivalence relation. (b) What are the distinct equivalence classes when m = 6? These are also known as the residue classes modulo 6 and the set of these residue classes is denoted by Ze.
2 Let Z be the set of integers and let m be a fixed positive integer. Define the relation by y if and only if m divides a- y (equivalently ay is a multiple of m). This is called the relation congruence modulo m in Z. (a) Prove that this relation is an equivalence relation. (b) What are the distinct equivalence classes when m = 6? These are also known as the residue classes modulo 6 and the set of these residue classes is denoted by Ze.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 8E: In Exercises 610, a relation R is defined on the set Z of all integers. In each case, prove that R...
Related questions
Question
Expert Solution
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 1 images
Recommended textbooks for you
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,