Directed Graphs: Reflexive, Symmetric, Transitive

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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/" [Broken]


Homework Equations



None


The Attempt at a Solution



In attachment + link.

Thanks.
 

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  • #2
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(1) and (4) are incorrect. The relation you graphed there are transitive.
 
  • #3
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(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.
 

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  • #4
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(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.
 
  • #5
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(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?
 
  • #6
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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)...
 
  • #7
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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?
 

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  • #8
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Yes, that looks fine!
 
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