1. For the set of all integer numbers Z one defines a relation R on Z as R = {(a, b)|a - b- 2 is divisible by 4} Find two distinct examples of pairs belonging to R. Determine which of the following properties this relation possesses: symmetry, anti-symmetry, reflexivity, transitivity. Jus- tify your answers either by counterexamples or by a general argument. Note that by definition 0 is divisible by any integer.
1. For the set of all integer numbers Z one defines a relation R on Z as R = {(a, b)|a - b- 2 is divisible by 4} Find two distinct examples of pairs belonging to R. Determine which of the following properties this relation possesses: symmetry, anti-symmetry, reflexivity, transitivity. Jus- tify your answers either by counterexamples or by a general argument. Note that by definition 0 is divisible by any integer.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 17E: In each of the following parts, a relation R is defined on the power set (A) of the nonempty set A....
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