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Relationship: reflexive, symmetric, antisymmetric, transitive

  1. Dec 17, 2012 #1
    1. The problem statement, all variables and given/known data
    Determine which binary relations are true, reflexive, symmetric, antisymmetric, and/or transitive.

    The relation R on P = {a, b, c} where R = {(a, a), (a, b), (a, c), (b, c), (c, b)}


    2. Relevant equations



    3. The attempt at a solution
    Not reflexive because there is no (b, b) or (c, c).
    Not symmetric because there is (a, b), but not (b, a).
    Not antisymmetric because there is (b, c) and (c, b).
    Not transitive because there is (b, c) and (c, b) but no (b, b).

    Is it possible for there to not be any binary relations?
     
  2. jcsd
  3. Dec 17, 2012 #2

    Dick

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    Science Advisor
    Homework Helper

    It is a binary relation, but as you say, it doesn't have any of those properties.
     
  4. Dec 17, 2012 #3
    Yeah, that's what I thought. Thanks for the help again.
     
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