4. Define a binary relation R on the set of integers Z by (a, b) E R if and only if |a – b| < 1. Is R reflexive? Is it symmetric? Is it antisymmetric? Is it transitive? Either show why the property holds or give a counterexample to show it is not.
4. Define a binary relation R on the set of integers Z by (a, b) E R if and only if |a – b| < 1. Is R reflexive? Is it symmetric? Is it antisymmetric? Is it transitive? Either show why the property holds or give a counterexample to show it is not.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 14E: In each of the following parts, a relation is defined on the set of all human beings. Determine...
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![4. Define a binary relation R on the set of integers Z by (a, b) E R if and only if |a – b| < 1. Is R
reflexive? Is it symmetric? Is it antisymmetric? Is it transitive? Either show why the property
holds or give a counterexample to show it is not.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8ced59ca-feed-4243-a114-dda1c615cc25%2Fe72c8b94-207f-47f1-beb9-0274585b3873%2Fsyfxmv_processed.png&w=3840&q=75)
Transcribed Image Text:4. Define a binary relation R on the set of integers Z by (a, b) E R if and only if |a – b| < 1. Is R
reflexive? Is it symmetric? Is it antisymmetric? Is it transitive? Either show why the property
holds or give a counterexample to show it is not.
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