Definition:Self-Distributive Operation

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

Then $\circ$ is self-distributive :


 * $(1): \quad \forall a, b, c \in S: \paren {a \circ b} \circ c = \paren {a \circ c} \circ \paren {b \circ c}$
 * $(2): \quad \forall a, b, c \in S: a \circ \paren {b \circ c} = \paren {a \circ b} \circ \paren {a \circ c}$

Also defined as
The term is sometimes used for operations for which only one of the above holds.

Also see

 * Self-Distributive Law for Conditional