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.”

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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