# Definition:Self Distributive

## Definition

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

Then $\circ$ is self-distributive if and only if:

• $\forall a, b, c \in S: \paren {a \circ b} \circ c = \paren {a \circ c} \circ \paren {b \circ c}$
• $\forall a, b, c \in S: a \circ \paren {b \circ c} = \paren {a \circ b} \circ \paren {a \circ c}$

## Also defined as

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