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2. Let S be a set, and ~R a relation on S. Suppose ~R is symmetric and transitive. Show that if for all x E S, there exists y ES such that ~ y, then ~R is also reflexive.

2. Let S be a set, and ~R a relation on S. Suppose ~R is symmetric and transitive. Show that if for all x E S, there exists y ES such that ~ y, then ~R is also reflexive.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 20E: Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not...
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2. Let S be a set, and a relation on S. Suppose~R is symmetric and transitive. Show that if for all x ES, there exists y ES such that Ry, then ~R is also reflexive.
Transcribed Image Text:2. Let S be a set, and a relation on S. Suppose~R is symmetric and transitive. Show that if for all x ES, there exists y ES such that Ry, then ~R is also reflexive.
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