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[Solved] relation on A that is symmetric and transitive but not reflexive

  1. Dec 1, 2011 #1
    1. The problem statement, all variables and given/known data
    Let A = {1,2,3,4}. Give an example of a relation on A that is symmetric and transitive, but not reflexive.

    2. Relevant equations
    Symmetric: if aRb then bRa
    Transitive: if aRb and bRc then aRc
    Reflexive: aRa for all a in A

    3. The attempt at a solution
    {(1,2),(2,1),(1,1)} It's symmetric because 1R2 and 2R1. Not reflexive because (2,2)...(4,4) are not elements and transitive because 1R2 and 2R1 so 1R1. Yet, this one got marked wrong on my homework. I'm going to assume my teacher is right, and I'm wrong. Can anyone find my mistake?
     
    Last edited: Dec 1, 2011
  2. jcsd
  3. Dec 1, 2011 #2

    jgens

    User Avatar
    Gold Member

    Re: Give an example of a relation on A that is symmetric and transitive but not refle

    2R1 and 1R2 implies 2R2 if your relation is transitive. But (2,2) isn't in A. So your teacher is right.
     
  4. Dec 1, 2011 #3
    Re: Give an example of a relation on A that is symmetric and transitive but not refle

    Oh wow, I can't believe I missed that! Thanks for that!
     
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