Directed Graphs: Reflexive, Symmetric, Transitive

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Homework Help Overview

The discussion revolves around the properties of directed graphs, specifically focusing on reflexivity, symmetry, and transitivity. The original poster seeks confirmation on their graphing of directed relations and has provided attachments for reference.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the correctness of the original poster's graphs, particularly questioning the transitive nature of certain relations. There are attempts to clarify why specific graphs are deemed incorrect and what properties they exhibit.

Discussion Status

The discussion is active, with participants providing feedback on the original poster's attempts. Some guidance has been offered regarding the definitions of transitivity and the conditions under which it applies, though there is still some uncertainty expressed by the original poster regarding their initial misunderstandings.

Contextual Notes

Participants are working within the constraints of homework rules, which may limit the amount of direct assistance provided. There is also a mention of misinterpretation of the questions, indicating potential gaps in understanding the properties of directed graphs.

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Homework Statement



Hello, I want to make sure that I graphed the directed graphs in my homework correctly. The problems and my work is located in the attachment. I also uploaded the directed graphs onto this link: http://img857.imageshack.us/f/83289329.png/"

Homework Equations



None

The Attempt at a Solution



In attachment + link.

Thanks.
 

Attachments

  • hw.jpg
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(1) and (4) are incorrect. The relation you graphed there are transitive.
 
micromass said:
(1) and (4) are incorrect. The relation you graphed there are transitive.

I do not understand why (4) is incorrect. But, I did changed somethings.
 

Attachments

  • hw.jpg
    hw.jpg
    4.8 KB · Views: 585
(4) is correct now. But (1) is still incorrect, since (1) is still transitive and it is not symmetric...

Transitive means: if you have an arrow from a to b, and an arrow from b to c, then you must have an arrow from a to c.
 
micromass said:
(4) is correct now. But (1) is still incorrect, since (1) is still transitive and it is not symmetric...

Transitive means: if you have an arrow from a to b, and an arrow from b to c, then you must have an arrow from a to c.

Woops... silly of me. I misread the question. Still I do not understand why the first time I did (1) and (4) I got it wrong.

(1) Is it because I excluded c from a to b and as a result, a to b is transitive?

(4) Is it because I gave them no relationships so a, b, c is nothing?
 
Well, transitive says that IF there is a relation between a and b, and b and c, THEN there is a relation between a and c.

But in your (4), there is no relation between a and b, and b and c, thus transitivity is satisfied. You only need to check transitivity whenever there is a relation, if there is no relation then it is trivially satisfied. Thesame with your (1)...
 
micromass said:
Well, transitive says that IF there is a relation between a and b, and b and c, THEN there is a relation between a and c.

But in your (4), there is no relation between a and b, and b and c, thus transitivity is satisfied. You only need to check transitivity whenever there is a relation, if there is no relation then it is trivially satisfied. Thesame with your (1)...

I see, then for (1), it should be something like this?
 

Attachments

  • Untitled.jpg
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Yes, that looks fine!
 
micromass said:
Yes, that looks fine!

Thank you very much.
 

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