Reflexive, Symmetric, or Transitive

[needhelp83]

Determine whether the following digraph represents a relation that is reflexive, symmetric, or transitive.

Not sure how to determine this. Any help would be wonderful. The digraph is uploaded into a word document.

 

[Defennder]

Do you think you could upload it in a PDF file instead? MS Word documents can be infected. Just print it to PDF.

 

[needhelp83]

Here you go. Now in PDF format

 

[HallsofIvy]

So that relation is {(1,2), (1, 4), (2,3), (2,4), (4,4)}.

Now what are the definitions of "reflexive, symmetric, and transitive"?

 

[needhelp83]

Let A be a set and R be a relation on A

R is reflexive on A iff for all x in A, x R x
R is symmetric iff for al x and y in A, if x R y, then y R x
R is transistive iff for all x, y, and z iin A, if x R y and y R z, then x R z

I have the definitions, but I am not quite sure that I can actually understand what is going on.

 

[HallsofIvy]

You relation is {(1,2), (1, 4), (2,3), (2,4), (4,4)}.

Let A be a set and R be a relation on A

R is reflexive on A iff for all x in A, x R x

"1" is certainly in "A". Is "1 R 1"- that is, is (1,1) in that relation?

R is symmetric iff for al x and y in A, if x R y, then y R x

(1, 2) is in that relation so "1 R 2". Is "2 R 1"? (Is (2, 1) in that relation?)

R is transistive iff for all x, y, and z iin A, if x R y and y R z, then x R z

(1, 2) and (2, 3) are in that relation so "1 R 2" and "2 R 3". Is "1 R 3"? (Is (1, 3) in that relation?

I have the definitions, but I am not quite sure that I can actually understand what is going on.

 

[needhelp83]

No none of these definitions fit for this relation. Thanks for the explanation by the way. That really helps me understand a lot better.

 

[needhelp83]

So did I interpret this correctly?

 

[HallsofIvy]

Yes, that is correct.