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Basic Set Theory: Determining Relations: Reflexive, Symmetric, Transitive

  1. Aug 24, 2012 #1
    I am taking a philosophy course that covers basic set theory as part of the introduction. I’m not sure in which section of the forum set theory should be, but I think this is the right place.

    1. The problem statement, all variables and given/known data

    For each of the following relations, indicate whether it is Reflexive, Nonreflexive, Irrelfexive, Symmetric, Nonsymmetric, Asymmetric, Antisymmetric, Transitive, Nontransitive, and Intransitive.

    9) {(b,d), (a,c), (d,c), (e,e), (b,c)} on the set {a,b,c,d,e}.

    2. Relevant equations
    3. The attempt at a solution

    I believe they are Nonreflexive, nonsymmetric, and transitive.

    I do not know if they are Asymmetric or Antisymmetric because I do not know how to deal with (e,e).
     
  2. jcsd
  3. Aug 25, 2012 #2

    HallsofIvy

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    You are correct that this relation is not symmetric because it contains (a, c) but not (c, a). It is not reflexive because it does not contain (a, a), (b, b), and (c, c). It is transitive because the only pairs of the form '(x, y), (y, z)' are (b, d) and (d, c) and it does contain (b, c). What is the difference between 'asymmetric' and 'antisymmetric'?
     
  4. Aug 25, 2012 #3

    Asymmetric: [itex]xRy \Rightarrow \neg (yRx) [/itex]

    Antisymmetric: [itex]xRy \wedge yRx \Rightarrow x=y [/itex]
     
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