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Reflexive, Symmetric, or Transitive

  1. Jun 29, 2008 #1
    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.
     

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    Last edited: Jun 29, 2008
  2. jcsd
  3. Jun 29, 2008 #2

    Defennder

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    Do you think you could upload it in a PDF file instead? MS Word documents can be infected. Just print it to PDF.
     
  4. Jun 29, 2008 #3
    Here you go. Now in PDF format
     
  5. Jun 29, 2008 #4

    HallsofIvy

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

    Now what are the definitions of "reflexive, symmetric, and transitive"?
     
  6. Jun 29, 2008 #5
    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.
     
  7. Jun 29, 2008 #6

    HallsofIvy

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    You relation is {(1,2), (1, 4), (2,3), (2,4), (4,4)}.
    "1" is certainly in "A". Is "1 R 1"- that is, is (1,1) in that relation?

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

    (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?

     
  8. Jun 30, 2008 #7
    No none of these definitions fit for this relation. Thanks for the explanation by the way. That really helps me understand alot better.
     
  9. Jun 30, 2008 #8
    So did I interpret this correctly?
     
  10. Jun 30, 2008 #9

    HallsofIvy

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    Yes, that is correct.
     
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