Explore BrainMass

Explore BrainMass

    Antisymmetric relations

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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.

    © BrainMass Inc. brainmass.com May 24, 2023, 12:48 pm ad1c9bdddf

    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.