Antiequivalence

An equivalence relation, as many of us already know, is defined as a relation which satisfies reflexivity, symmetry, and transitivity. This afternoon, I was musing about an "antiequivalence relation": a relation which is irreflexive (for all a, a R a is never true), antisymmetric (for all a and b, if a R b, then b R a is false) and intransitive (for all a, b, and c, if a R b and b R c, then a R c is false). And, after some thought, we came up with one: "a is the biological mother of b".

For some reason, I felt the need to share this.