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An example of a relation that is symmetric and anti-symmetric

  1. Apr 5, 2015 #1
    Would this example be valid in satisfying a relation that is symmetric and anti-symmetric?

    The relation R = {(1,1),(2,2)} on the set A = {1,2,3}

    Also, i'm curious to know since relations can both be neither symmetric and anti-symmetric, would R = {(1,2),(2,1),(2,3)} be an example of such a relation? (I'm unsure if I'm using the definitions correctly).
     
  2. jcsd
  3. Apr 5, 2015 #2

    wabbit

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    Gold Member

    Yes, and that's essentially the only case : If R is both symmetric and antisymmetric then R must be the relation ## \{(x,x),x \in B\} ## for some subset ## B\subset A ##.
    Yes. Symmetric or antisymmetric are special cases, most relations are neither (although a lot of useful/interesting relations are one or the other).
     
    Last edited: Apr 5, 2015
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