# 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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#### 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.

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