Question

Set Theory (Reflexive, Symmetric, Transitive)

Asked by: ExpExchHelp

I am taking a class that covers "set theory".    Please see attached JPG (question) and PDF (my answer).

I have no trouble following the function "R" (first function).   As the PDF shows, the answer is "yes" to all... reflexive, symmetry, and transitive.

However, I'm not fully clear on the function "S" (second function).   In the PDF, I drew the relation (3,1) in red dotted lines.

My questions:
1. As I don't have a relation (arrow) for (3,2), should I NOT have drawn the relation (3,1)?   In other words, as I cannot get from (3,2), I could not get from (3,1).   So, again, should I remove the red dotted line?

2. In my opinion, there is no symmetry as (3,2) does NOT exist.   If I do have to remove the red dotted line, do I then also have to remove the transitive relation (1,3)?    In other words, given that I cannot get back from (3,1), should I even go from (1,3)?

Thanks, I appreciate any hints on that?

EEH

This Question has been solved and asker verified All Experts Exchange premium technology solutions are available to subscription members.

Subscribe now for full access to Experts Exchange and get

Instant Access to this Solution

  • Plus...
  • 30 Day FREE access, no risk, no obligation
  • Collaborate with the world's top tech experts
  • Unlimited access to our exclusive solution database
  • Never be left without tech help again

Subscribe Now

Asked On
2009-09-18 at 05:57:06ID24743046
Topics

Math & Science

,

Probability & Statistics

Participating Experts
1
Points
500
Comments
5

Trusted by hundreds of thousands everyday for fast, accurate and reliable tech support.

  • "The time we save is the biggest benefit of Experts Exchange to Warner Bros. What could take multiple guys 2 hours or more each to find is accessed in around 15 minutes on Experts Exchange." Mike Kapnisakis, Warner Bros.
  • "Our team likes having a resource that is more secure than just using Google and most experts using this service really know their stuff. It's nice to look here first versus using Google." Dayna Sellner, Lockheed Martin
  • "Anytime that I've been stumped with a problem, 9 out of 10 times Experts Exchange has either the accepted solution or an open discussion of the potential solution to the problem." Kenny Red, eBay Inc.

See what Experts Exchange can do for you.

Got a question?

We've got the answer.

Experts Exchange has been collecting answers to technology questions since 1996…3 million and counting! If you have a question, chances are we already have your answer.

Screenshot of Experts Exchange Knowledgebase

Need individual assistance?

Our experts are ready to help.

If you can't find the exact answer you're looking for, ask our exclusive community of 50,000 experts. You’ll get a personalized answer from a trusted professional.

Screenshot of Experts Exchange Knowledgebase

Want to learn from the best?

Read articles from industry experts.

Thousands of free tech tips, tricks, how-to’s and tutorials are available in our peer reviewed articles section. See for yourself how smart our experts are, no login required.

Screenshot of an Article

Working on a long term project?

Store your work and research.

Save solutions to your questions, answers you’ve discovered through searching plus helpful articles in your personal knowledgebase for easy future access.

Screenshot of Experts Exchange Knowledgebase

Access the answers to your technology questions today.

Subscribe Now

30-day free trial. Register in 60 seconds.

What Makes Experts Exchange Unique?

Members of the expert community talk about why the experience at Experts Exchange is different than what you will find anywhere else.

Trusted by the world's most respected brands.

image of each brand's logo

Faithfully serving IT professionals since 1996.

Experts Exchange Logo

Try it out and discover for yourself.

Subscribe Now

30-day free trial. Register in 60 seconds.

Related Solutions

  1. covering theory and covering design theorem
    there is a program called lottogenius at www.lottogenius.com it works on the covering theory and covering design theorem has anybody got any code in any programming language (vb preferred) so that i can see how this works? i'd like to make my own lotto genius. Is there...
  2. Optical sorting theory
    I have an idea which may be way beyond my capabilities...but that never stopped me before ;) I have an application for some type of scanner/camera which would monitor small (12mm x 3mm cylinders approx) items on a conveyor 99.3% of these items would be within a close colou...

Free Tech Articles

  1. WARNING: 5 Reasons why you should NEVER fix a computer for free.
    It is in our nature to love the puzzle. We are obsessed. The lot of us. We love puzzles. We love the challenge. We thrive on finding the answer. We hate disarray. It bothers us deep in our soul. W...
  2. SCCM OSD Basic troubleshooting
    SCCM 2007 OSD is a fantastic way to deploy operating systems, however, like most things SCCM issues can sometimes be difficult to resolve due to the sheer volume of logs to sift through and the dispe...
  3. Migrate Small Business Server 2003 to Exchange 2010 and Windows 2008 R2
    This guide is intended to provide step by step instructions on how to migrate from Small Business Server 2003 to Windows 2008 R2 with Exchange 2010. For this migration to work you will need the fo...
  4. Create a Win7 Gadget
    This article shows you how to create a simple "Gadget" -- a sort of mini-application supported by Windows 7 and Vista. Gadgets can be dropped anywhere on the desktop to provide instant information, ...
  5. Outlook continually prompting for username and password
    There have been a lot of questions recently regarding Outlook prompting for a username and password whilst using Exchange 2007. There are a few reasons why this would happen and I will try to cover t...
  6. Backup Exchange 2010 Information Store using Windows Backup
    There seems to be quite a lot of confusion around the ability to backup Exchange 2010 using the built in Windows Backup feature. This stems from the omission of this feature prior to Exchange 2007 s...

Cloud Class Webinars

  1. Avoiding Bugs in Microsoft Access
    Alison Balter takes and in-depth look at avoiding bugs in Access. In this webinar you will learn about using the immediate window to debug your applications, invoking the debugger, using breakpoints to troubleshoot, stepping through code, setting the next statement to execute, ...
  2. Top 10 Best New Features in Visio 2010
    Scott Helmers gives live demonstrations of the top 10 new features in Visio 2010. This webinar will teach you how to create compelling diagrams by adding shapes to the page with a single click, linking the shapes in a diagram to data in Excel (or SQL Server, or SharePoint), ...
  3. IT Consultant Business Secrets Revealed
    Michael Munger, Experts Exchange tech pro and IT consultant, pulls back the curtain on his very successful businesses and answers question on every IT consultant and business owner should know about. He shares secrets on what he did to solve the 5 most common problems in IT, ...
  4. Disaster Recovery and Business Continuity
    Quest CTO, Mike Billon, gives an overview of the steps involved in building a dunamic disaster recovery plan. Through case studies and an examination of software/hardware tooles for monitoring and testing, you'll gain a better understandin of where you are, where you want ...
  5. Organize Your Visio Diagrams with Containers and Lists
    Scott Helmers uses cross functional flowcharts, wireframe diagrams, data graphic legends and seating charts to teach you: how to ustilize all three new structured diagram components in Visio 2010, the best practices for organizeing shapes in previous version of Visio, how to organize ...
  6. How to Us Objects, Properties, Events and Methods in Microsoft Access
    Alison Dalter gives an in-depbth look at objects, properties, events and methods in Microsoft Access. In this webinar you will learn about using the object browser, referring to objects, working with properties and methods, working with object variables, understanding the ...

Join the Community

Give a Little. Get a Lot.

Join the community of experts here and help other tech pros by answering question in your area of expertise. You can earn FREE access to all Experts Exchange's premium features and resources.

Join the Community

Answers

 

by: thehagmanPosted on 2009-09-18 at 07:47:35ID: 25366520

S not symmetric, not reflexive, not transitive
However your argument needs clarification (esp. the blue arrow makes no sense to me):
To show that S is not transitive sou need to find just one triplet a,b,c such that
(a,b) in S
(b,c) in S
(a,c) not in S
We have (3,1) and (1,2), but not (3,2)
I think You try to argue: We don't have (3,2) and we have (1,2), hence we should not have (3,1) - this is ok, but somewhat confusing.

 

by: ExpExchHelpPosted on 2009-09-18 at 08:10:23ID: 25366769

thehagman:

Ok, I'm sure it's me... I just want to understand the conceptual approach.    Let me start by explaining my understanding of "symmetry".

If I have (1,2) and (2,1)... I have symmetry.
If I have (1,2), and (2,1) and (2,3) but not (3,2), I don't have "big picture" symmetry (balance), right.    

Applying that "big picture balance), I tried to understand if I need to apply this also for transitivity.
Yes, as I can go from (1,2) and (2,4), I have transitivity from (1,3).
On the other hand, as (3,2) is missing, I don't have transitity for (3,1).
Now, giving that I don't have transitivity on the "bottom" do I still have transitivity on the "top"?  
My view is not "balanced", right?

Is that's why you indicated there the S function does NOT have eitehr symmetry, reflexivity, and transitivity?

EEH

 

by: ExpExchHelpPosted on 2009-09-18 at 14:30:55ID: 25370149

thehagman:

quick follow-up... some of your comments don't "click" (for me).

Yes, I agree, S is NOT symmetric and NOT reflexive.  I'm just not too sure about the transitive portion.

For a moment, forget about the colors (e.g. "esp. the blue arrow makes no sense to me").

Based on the 2nd diagram, all relations are drawn:  S = {(2, 3), (1, 2), (2, 1), (3, 1), (1, 3)}

What I don't understand is the following:

1. While (3, 1) is given, should it or should it NOT be drawn?  Why?  (3,2) doesn't exist, so logically (3,1) shouldn't exist, right?

2. If #1 is a correct assumption, do I the leave (1,3) untouched (making it a "one-way relationship") or should it also be removed?  

Again, given that (3,2) does not exist, I'm not sure if the provided relationships (1,3) and (3,1) should be included or excluded.

Finally, assuming that I should leave (1,3) in the graph, does this "one-way" relationship is the key for THE GRAPH IS NOT TRANSITIVE?

Thanks,
EEH

 

by: ExpExchHelpPosted on 2009-09-19 at 16:05:04ID: 31630519

Never followed up w/ another response.

 

by: thehagmanPosted on 2009-09-20 at 01:23:39ID: 25376284

Post-mortem clarification:
Ad 1: Sometimes, when representing a relation by arrows, one may try to do so in an economic manner, that is not draw all arrows, but only the essential ones. For example *IF* the relation is known to be transitive, one *MAY* leave out any arrows that can be inferred by transitivity and tell the reader that these are omitted (but formally the arrows *are* there, this methos is just a kind of shortcut to avoid spaghetti pictures).
In principle, all arrows a-> b belonging o pairs (a,b) in R should be drawn. Especially in this case, where the transitivity i sat doubt, such a shortcut method should not be used.

I guess you get the idea for #2 then as well.

20120131-EE-VQP-002

3 Ways to Join

30-Day Free Trial

The Experts

98% positive feedback on 31,087 answers since March 2000. angeliii is a Microsoft Most Valuable Professional for his work with MS SQL Server & Develoment.

He has also proven his knowledge of Visual Basic Programming, PHP Scripting and Oracle Databases.

The Experts

97% positive feedback on 10,752 answers since July 2000. lrmoore has more than 18 years experience in the networking industry.

The six-time Mircosoft MVPs specialties include firewalls, virtual private networking, and network management.

Testimonials

"...and excellent source for support... Kind of like having your very own IT dept." Electriciansnet

Testimonials

"I was apprehensive at signing up at first. However... it has already made my life as an IT administrator much easier." JaCrews

Testimonials

"WOW! You guys have great, active, and knowledgeable people on here." moore50

Business Clients

Business Clients

In the Press

"If you’ve got a question... Experts Exchange can supply an answer.”

In the Press

"...an invaluable aid for both IT professionals and those who require tech support."

In the Press

"where IT professionals provide quick answers on just about any topic"

Business Account Plans

Loading Advertisement...