on the subsets of any given set is antisymmetric: given two sets and if every element in also is in and every element in is also in then and must contain all the same elements and therefore be equal:

A real-life example of a relation that is typically antisymmetric is "paid the restaurant bill of" (understood as restricted to a given occasion). Typically, some people pay their own bills, while others pay for their spouses or friends. As long as no two people pay each other's