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    Antisymmetric relations

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    Let R and S be antisymmetric relations on a set A. Does R union S have to be antisymmetric also? Give a counterexample if the answer is no and proof if it is yes.

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    https://brainmass.com/math/linear-algebra/antisymmetric-relations-2491

    Solution Preview

    Let R and S be relations as defined below:
    R={(a,b)} and S={(b,a)}
    Note that they are both antisymmetric relations.
    >But R U S = {(a,b),(b,a)} is ...

    Solution Summary

    This is a proof regarding antisymmetric relations. The proof with counter examples and antisymmetric relations are given.

    $2.49

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