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Math Help - antisymmetric

  1. #1
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    antisymmetric

    R = {(a,b) is an element of A cross B with (b,a) an element of R inverse}

    Proof:
    If R is antisymmetric, then R inverse is antisymmetric

    -if you can not prove this I must show a counterexample thanks
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  2. #2
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    You need to show if R is antisymettric, meaning if a<=b and b<=a implies a=b. Then R^{-1} has the same property. It should be clear how to do this by definition.
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  3. #3
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    If (x,y) \in R^{ - 1}  \wedge (y,x) \in R^{ - 1} \quad  \Rightarrow \quad (y,x) \in R \wedge (x,y) \in R.
    But we know that R is antisymmetric so x=y.
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