1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook