1. Let R be the relation on N defined by "aRb if EN or 5| (b – a)". So for example (6,2) € R and (1,5) ¢ R . Decide if each of the following are true or false, and briefly justify each answer. (a) R is reflexive (b) R is symmetric (c) R is antisymmetric (d) R is transitive

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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1.
Let R be the relation on N defined by "aRb if EN or 5| (b – a)".
So for example (6,2) € R and (1,5) ¢ R .
Decide if each of the following are true or false, and briefly justify each answer.
(a) R is reflexive
(b) R is symmetric
(c) R is antisymmetric
(d) R is transitive
Transcribed Image Text:1. Let R be the relation on N defined by "aRb if EN or 5| (b – a)". So for example (6,2) € R and (1,5) ¢ R . Decide if each of the following are true or false, and briefly justify each answer. (a) R is reflexive (b) R is symmetric (c) R is antisymmetric (d) R is transitive
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