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.

© SolutionLibrary Inc. solutionlibary.com 9836dcf9d7 https://solutionlibrary.com/math/algebra/antisymmetric-relations-2dr

Solution Preview

...symmetry means that the only case where xRy ^ yRx can occur is if
x=y. So it allows for (but not required to have) xRx in the relation
but not both of xRz and ...