Answered: 2. Define a relation R on Z as follows:…

2. Define a relation R on Z as follows: a Rb if and only if 5 | (a²-b²). a) Prove that R is an equivalence relation (that is, prove each of the three properties).

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 28E

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Question

2. Define a relation R on Z as follows: a Rb if and only if 5 | (a² – b²).
a) Prove that R is an equivalence relation (that is, prove each of the three properties).

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