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1. Prove that the relation "divides" on the integers is reflexive and transitive.

1. Prove that the relation "divides" on the integers is reflexive and transitive.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...
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1. Prove that the relation "divides" on the integers is reflexive and transitive. 2. Let A = {0, 1, 2, 3) and let r = {(0, 0), (1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (3, 0), (0, 3) } be a relation on A. Show that r is an equivalence relation, list all the equivalence classes, and explain why the equivalence classes form a partition of A Thank you!
Transcribed Image Text:1. Prove that the relation "divides" on the integers is reflexive and transitive. 2. Let A = {0, 1, 2, 3) and let r = {(0, 0), (1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (3, 0), (0, 3) } be a relation on A. Show that r is an equivalence relation, list all the equivalence classes, and explain why the equivalence classes form a partition of A Thank you!
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