1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    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!

True Or False: Symmetry, anti-symmetric, asymmetry.

  1. May 19, 2013 #1
    1. The problem statement, all variables and given/known data

    State whether the following are true or false. If false, give a counter-example:

    1. ≽ is not symmetric [itex]\Rightarrow[/itex] ≽ is not asymmetric
    2. ≽ is not symmetric [itex]\Rightarrow[/itex] ≽ is not antisymmetric
    3. ≽ is not antisymmetric [itex]\Rightarrow[/itex] ≽ is not asymmetric

    2. Relevant equations

    Symmetric:
    For any x,y[itex]\in[/itex]X, x≽y [itex]\Rightarrow[/itex] y≽x

    Antisymmetric:
    For any x,y[itex]\in[/itex]X, x≽y and y≽x and x=y

    Asymmetric:
    For any x,y[itex]\in[/itex]X, x≽y[itex]\neq[/itex]y≽x

    3. The attempt at a solution

    1. False. Lack of symmetry does not mean you can't be asymmetrical. Lack of symmetry in which x≽y [itex]\neq[/itex]y≽x is the very definition of anti-symmetry.

    2. False. Lacking symmetry does not mean you lack anti-symmetry. I don't know how to explain this one.

    3. True. A relation is asymmetric if and only if it is anti-symmetric. I can however, be anti-symmetric and not be asymmetric.

    Could you guys look this over and give me some guidance on number 2?
     
  2. jcsd
  3. May 19, 2013 #2

    verty

    User Avatar
    Homework Helper

    Hint: When you have "not" on both sides of the implication, use the contrapositive instead.
     
  4. May 19, 2013 #3
    Okay. So by that I assume you mean just prove that when I am anti-symmetric, I can be symmetric.

    So could I say that given the set X: {(1,1)} in ℝ Is both anti-symmetric and symmetric?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: True Or False: Symmetry, anti-symmetric, asymmetry.
  1. True / False (Replies: 4)

  2. True or false (Replies: 7)

  3. Calc vertice problem (Replies: 1)

Loading...