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Let A be a set and R be a reflexive relation on A. Prove that R is an equivalence relation if and only if for any a,b,c ∈ A, (a,b),(a,c) ∈ R implies (b,c)∈ R

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 10E: In Exercises , a relation is defined on the set of all integers. In each case, prove that is an...

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Let A be a set and R be a reflexive relation on A. Prove that R is an equivalence relation if and only if for any a,b,c ∈ A, (a,b),(a,c) ∈ R implies (b,c)∈ R

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