Definition:Antiassociative Operation

Definition
Let $\circ$ be a binary operation on the set $S$.

$\circ$ is said to be antiassociative on $S$ iff:


 * $\forall x, y, z \in S: \left({x \circ y}\right)\circ z \ne x \circ \left({y \circ z}\right)$

Example
A non-trivial example is given here.