We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Theory of Positive Integers : Function & Equivalence Relations

Study concepts, example questions & explanations for Theory of Positive Integers

Create An Account

All Theory of Positive Integers Resources

5 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Function & Equivalence Relations

Which of the following is a property of a relation?

Possible Answers:

Equivalency Property

All are properties of a relation

Non-symmetric Property

Partition Property

Symmetric Property

Correct answer:

Symmetric Property

Explanation:

For a relation to exist there must be a non empty set present. If a non empty set is present then there are three relation properties.

These properties are:

I. Reflexive Property

$x\approx x$

II. Symmetric Property

$x\approx y\rightarrow y\approx x$

III. Transitive Property

$x\approx y, y\approx z \rightarrow x\approx z$

When all three properties represent a specific set, then that set is known to have an equivalence relation.

Report an Error

Example Question #1 : Function & Equivalence Relations

What is an equivalency class?

Possible Answers:

$[x]=\begin{Bmatrix} y\ \epsilon\ A, -x\approx y \end{Bmatrix}$

$[x]=\begin{Bmatrix} y\ \epsilon\ A, x\approx y \end{Bmatrix}$

$[x]=\begin{Bmatrix} y\ \epsilon\ A\end{Bmatrix}$

$[x]=\begin{Bmatrix} y\ \epsilon\ A, x>y \end{Bmatrix}$

$[x]=\begin{Bmatrix} x\approx y \end{Bmatrix}$

Correct answer:

$[x]=\begin{Bmatrix} y\ \epsilon\ A, x\approx y \end{Bmatrix}$

Explanation:

An equivalency class is a definitional term.

Suppose is a non empty set and $\approx$ is an equivalency relation on . Then belonging to is a set that holds all the elements that live in that are equivalent to .

In mathematical terms this looks as follows,

$[x]=\begin{Bmatrix} y\ \epsilon\ A, x\approx y \end{Bmatrix}$

Report an Error

Example Question #2 : Function & Equivalence Relations

Which of the following is a property of a relation?

Possible Answers:

Reflexive Property

All are relation properties

Associative Property

Non-symmetric Property

Equivalency Property

Correct answer:

Reflexive Property

Explanation:

For a relation to exist there must be a non empty set present. If a non empty set is present then there are three relation properties.

These properties are:

I. Reflexive Property

$x\approx x$

II. Symmetric Property

$x\approx y\rightarrow y\approx x$

III. Transitive Property

$x\approx y, y\approx z \rightarrow x\approx z$

When all three properties represent a specific set, then that set is known to have an equivalence relation.

Report an Error

Example Question #3 : Function & Equivalence Relations

Which of the following is a property of a relation?

Possible Answers:

Non-symmetric Property

Partition Property

All are properties of relations.

Equivalency Property

Transitive Property

Correct answer:

Transitive Property

Explanation:

For a relation to exist there must be a non empty set present. If a non empty set is present then there are three relation properties.

These properties are:

I. Reflexive Property

$x\approx x$

II. Symmetric Property

$x\approx y\rightarrow y\approx x$

III. Transitive Property

$x\approx y, y\approx z \rightarrow x\approx z$

When all three properties represent a specific set, then that set is known to have an equivalence relation.

Report an Error

View Tutors

Madelyn
Certified Tutor

University of Central Florida, Bachelor in Arts, Writing, General.

View Tutors

Polly
Certified Tutor

View Tutors

Shubham
Certified Tutor

Jaypee University of Information and Technology, Bachelor of Technology, Computer Science.

All Theory of Positive Integers Resources

5 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ACT Tutors in Seattle, Calculus Tutors in Los Angeles, LSAT Tutors in Los Angeles, Reading Tutors in Miami, French Tutors in Washington DC, MCAT Tutors in San Diego, MCAT Tutors in Houston, Spanish Tutors in Atlanta, Physics Tutors in Seattle, ACT Tutors in Philadelphia

Popular Courses & Classes

GMAT Courses & Classes in New York City, LSAT Courses & Classes in Los Angeles, GMAT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Seattle, GMAT Courses & Classes in Philadelphia, GMAT Courses & Classes in Houston, ISEE Courses & Classes in San Diego, ACT Courses & Classes in Los Angeles, GRE Courses & Classes in Washington DC, SAT Courses & Classes in Houston

Popular Test Prep

ISEE Test Prep in San Diego, ACT Test Prep in Washington DC, ISEE Test Prep in Miami, ACT Test Prep in Los Angeles, GRE Test Prep in Seattle, ISEE Test Prep in Phoenix, SAT Test Prep in Phoenix, ISEE Test Prep in Houston, SSAT Test Prep in Washington DC, GMAT Test Prep in Miami

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Theory of Positive Integers : Function & Equivalence Relations

Study concepts, example questions & explanations for Theory of Positive Integers

All Theory of Positive Integers Resources

Example Questions

Example Question #1 : Function & Equivalence Relations

Example Question #1 : Function & Equivalence Relations

Example Question #2 : Function & Equivalence Relations

Example Question #3 : Function & Equivalence Relations

All Theory of Positive Integers Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: