Answered: Let A be a set and R be a symmetric and…

Let A be a set and R be a symmetric and transitive relation on A. Prove the following statement: If for all a ∈ A, there exists b ∈ A with (a,b) ∈ R, then R is an equivalence relation.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.3: Divisibility

Problem 18E: Let R be the relation defined on the set of integers by aRb if and only if ab. Prove or disprove...

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Let A be a set and R be a symmetric and transitive relation on A. Prove the following statement:

If for all a ∈ A, there exists b ∈ A with (a,b) ∈ R, then R is an equivalence relation.

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