# Antisymmetric relations

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.

Â© BrainMass Inc. brainmass.com March 4, 2021, 5:36 pm ad1c9bdddfhttps://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