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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 all integers where aRy is |a-b|<=3


    2. Relevant equations



    3. The attempt at a solution
    The relationship is reflexive because any number minus itself will be zero which is less than 3.
    The relationship is symmetric because whenever |a-b|<=3 then |b-a|<=3 is also true.
    The relationship is not antisymmetric. Consider (2, 1) and (1, 2). Int his case, |2-1|<=3 and |1-2|<=3.
    The relationship is not transitive. Consider (4, 1) and (1, 0). |4-1|<=3 and |1-0|<=3, but |4-0| is not <= 3.

    I just want to make sure I'm understanding this correctly. Is this right or am I missing something? I can't think of a case where the relationship wouldn't be symmetric.
     
    Last edited: Dec 17, 2012
  2. jcsd
  3. Dec 17, 2012 #2

    Dick

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    Science Advisor
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    Those all look correct to me.
     
  4. Dec 17, 2012 #3
    Thank you for the reassurance.
     
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