6. Let S be a set and supposeprovide a counterexample.~is a relation on S. For each of the following,is reflexive and symmetric, is it transitive?(a) If(b) If is reflexive and transitive, is it symmetric?1(c) If is symmetric and transitive, is it reflexive?

Let us solve the given problems on relation in the next steps.

Answered: 6. Let S be a set and suppose is a…

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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6. Let S be a set and suppose is a relation on S. For each of the following, provide a counterexample. (a) If (b) If (c) If ~ is reflexive and symmetric, is it transitive? is reflexive and transitive, is it symmetric? 1 is symmetric and transitive, is it reflexive?