How can I prove that the relationship r^2 is a subset of r using the definition of composition? 8.(a) Prove that if r is a transitive relation on a set A, then r² Cr.(b) Find an example of a transitive relation for which r² #r.

The objective of this question is to prove that if r is a transitive relation on a set A, then r^2…

Answered: 8. (a) Prove that if r is a transitive…

8. (a) Prove that if r is a transitive relation on a set A, then r² Cr. (b) Find an example of a transitive relation for which r² #r.

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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Question

How can I prove that the relationship r^2 is a subset of r using the definition of composition?

8.
(a) Prove that if r is a transitive relation on a set A, then r² Cr.
(b) Find an example of a transitive relation for which r² #r.

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