BuyFindarrow_forward

Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230

Solutions

Chapter
Section
BuyFindarrow_forward

Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
Textbook Problem
3 views

Label each of the following statements as either true or false.

Let R be a relation on a nonempty set A that is symmetric and transitive. Since R is symmetric x R y implies y R x . Since R is transitive x R y and y R x implies x R x . Hence R is alsoreflexive and thus an equivalence relation on A .

To determine

Whether the statement, “Let R be a relation on nonempty set A that is symmetric and transitive. Since R is symmetric xRy implies that yRx. Since R is transitive xRy and yRx implies that xRx. Hence R is reflexive and thus an equivalence relation on set A ” is true or false.

Explanation

Consider the statement, “Let R be a relation on nonempty set A that is symmetric and transitive. Since R is symmetric xRy implies that yRx. Since R is transitive xRy and yRx implies that xRx. Hence R is reflexive and thus an equivalence relation on set A ”.

Counter example:

Let A={a,b,c}

Let R={(a,a),(a,b),(b,a),(b,b)} is relation on set A.

For (a,a)R implies that (a,a)R

For (a,b)R implies that (b,a)R

For (b,a)R implies that (a,b)R

For (b,b)R implies that (b,b)R

Thus the relation R is symmetric

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started
Sect-1.1 P-1ESect-1.1 P-2ESect-1.1 P-3ESect-1.1 P-4ESect-1.1 P-5ESect-1.1 P-6ESect-1.1 P-7ESect-1.1 P-8ESect-1.1 P-9ESect-1.1 P-10ESect-1.1 P-11ESect-1.1 P-12ESect-1.1 P-13ESect-1.1 P-14ESect-1.1 P-15ESect-1.1 P-16ESect-1.1 P-17ESect-1.1 P-18ESect-1.1 P-19ESect-1.1 P-20ESect-1.1 P-21ESect-1.1 P-22ESect-1.1 P-23ESect-1.1 P-24ESect-1.1 P-25ESect-1.1 P-26ESect-1.1 P-27ESect-1.1 P-28ESect-1.1 P-29ESect-1.1 P-30ESect-1.1 P-31ESect-1.1 P-32ESect-1.1 P-33ESect-1.1 P-34ESect-1.1 P-35ESect-1.1 P-36ESect-1.1 P-37ESect-1.1 P-38ESect-1.1 P-39ESect-1.1 P-40ESect-1.1 P-41ESect-1.1 P-42ESect-1.1 P-43ESect-1.2 P-1TFESect-1.2 P-2TFESect-1.2 P-3TFESect-1.2 P-4TFESect-1.2 P-5TFESect-1.2 P-6TFESect-1.2 P-7TFESect-1.2 P-8TFESect-1.2 P-9TFESect-1.2 P-1ESect-1.2 P-2ESect-1.2 P-3ESect-1.2 P-4ESect-1.2 P-5ESect-1.2 P-6ESect-1.2 P-7ESect-1.2 P-8ESect-1.2 P-9ESect-1.2 P-10ESect-1.2 P-11ESect-1.2 P-12ESect-1.2 P-13ESect-1.2 P-14ESect-1.2 P-15ESect-1.2 P-16ESect-1.2 P-17ESect-1.2 P-18ESect-1.2 P-19ESect-1.2 P-20ESect-1.2 P-21ESect-1.2 P-22ESect-1.2 P-23ESect-1.2 P-24ESect-1.2 P-25ESect-1.2 P-26ESect-1.2 P-27ESect-1.2 P-28ESect-1.3 P-1TFESect-1.3 P-2TFESect-1.3 P-3TFESect-1.3 P-4TFESect-1.3 P-5TFESect-1.3 P-6TFESect-1.3 P-1ESect-1.3 P-2ESect-1.3 P-3ESect-1.3 P-4ESect-1.3 P-5ESect-1.3 P-6ESect-1.3 P-7ESect-1.3 P-8ESect-1.3 P-9ESect-1.3 P-10ESect-1.3 P-11ESect-1.3 P-12ESect-1.4 P-1TFESect-1.4 P-2TFESect-1.4 P-3TFESect-1.4 P-4TFESect-1.4 P-5TFESect-1.4 P-6TFESect-1.4 P-7TFESect-1.4 P-8TFESect-1.4 P-9TFESect-1.4 P-1ESect-1.4 P-2ESect-1.4 P-3ESect-1.4 P-4ESect-1.4 P-5ESect-1.4 P-6ESect-1.4 P-7ESect-1.4 P-8ESect-1.4 P-9ESect-1.4 P-10ESect-1.4 P-11ESect-1.4 P-12ESect-1.4 P-13ESect-1.4 P-14ESect-1.4 P-15ESect-1.4 P-16ESect-1.5 P-1TFESect-1.5 P-2TFESect-1.5 P-3TFESect-1.5 P-1ESect-1.5 P-2ESect-1.5 P-3ESect-1.5 P-4ESect-1.5 P-5ESect-1.5 P-6ESect-1.5 P-7ESect-1.5 P-8ESect-1.5 P-9ESect-1.5 P-10ESect-1.6 P-1TFESect-1.6 P-2TFESect-1.6 P-3TFESect-1.6 P-4TFESect-1.6 P-5TFESect-1.6 P-6TFESect-1.6 P-7TFESect-1.6 P-8TFESect-1.6 P-9TFESect-1.6 P-10TFESect-1.6 P-11TFESect-1.6 P-12TFESect-1.6 P-1ESect-1.6 P-2ESect-1.6 P-3ESect-1.6 P-4ESect-1.6 P-5ESect-1.6 P-6ESect-1.6 P-7ESect-1.6 P-8ESect-1.6 P-9ESect-1.6 P-10ESect-1.6 P-11ESect-1.6 P-12ESect-1.6 P-13ESect-1.6 P-14ESect-1.6 P-15ESect-1.6 P-16ESect-1.6 P-17ESect-1.6 P-18ESect-1.6 P-19ESect-1.6 P-20ESect-1.6 P-21ESect-1.6 P-22ESect-1.6 P-23ESect-1.6 P-24ESect-1.6 P-25ESect-1.6 P-26ESect-1.6 P-27ESect-1.6 P-28ESect-1.6 P-29ESect-1.6 P-30ESect-1.6 P-31ESect-1.6 P-32ESect-1.7 P-1TFESect-1.7 P-2TFESect-1.7 P-3TFESect-1.7 P-4TFESect-1.7 P-5TFESect-1.7 P-6TFESect-1.7 P-1ESect-1.7 P-2ESect-1.7 P-3ESect-1.7 P-4ESect-1.7 P-5ESect-1.7 P-6ESect-1.7 P-7ESect-1.7 P-8ESect-1.7 P-9ESect-1.7 P-10ESect-1.7 P-11ESect-1.7 P-12ESect-1.7 P-13ESect-1.7 P-14ESect-1.7 P-15ESect-1.7 P-16ESect-1.7 P-17ESect-1.7 P-18ESect-1.7 P-19ESect-1.7 P-20ESect-1.7 P-21ESect-1.7 P-22ESect-1.7 P-23ESect-1.7 P-24ESect-1.7 P-25ESect-1.7 P-26ESect-1.7 P-27ESect-1.7 P-28ESect-1.7 P-29ESect-1.7 P-30E

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

The profit P (in dollars) of a one product company is given by P = g(x), where x is the number of units sold. A...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Evaluate the definite integral. /3/3x4sinxdx

Single Variable Calculus: Early Transcendentals, Volume I

Add the following signed number: (+4)+(4)

Elementary Technical Mathematics

Finding a Derivative In Exercises 133-148, find the derivative of the function. g(x)=5x

Calculus: Early Transcendental Functions (MindTap Course List)

The harmonic series is: 1 + 2 + 3 + 4 + …

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Find the unit tangent vector for at t = –1.

Study Guide for Stewart's Multivariable Calculus, 8th

What are the five steps of the scientific method?

Research Methods for the Behavioral Sciences (MindTap Course List)