Problem 2 Let A be a set, and let R be a relation on A. Suppose that R is symmetric and transitive. Find the flaw in the following alleged proof that this relation is necessarily reflexive. “Let x ∈A. Choose y ∈A such that xRy. By symmetry know that yRx, and then by transitivity we see that xRx. Hence R is reflexive.”

Problem 2 Let A be a set, and let R be a relation on A. Suppose that R is symmetric and transitive. Find the flaw in the following alleged proof that this relation is necessarily reflexive. “Let x ∈A. Choose y ∈A such that xRy. By symmetry know that yRx, and then by transitivity we see that xRx. Hence R is reflexive.”

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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