For two [[Binary Operation|binary operations]] $\circ$ and $\triangleright$, we say that $\circ$ is [[Distributive Property|distributive]] over $\triangleright$ [[Biconditional|if and only if]] $\circ$ is both [[Left Distributive Property|left distributive]] and [[Right Distributive Property|right distributive]] over $\triangleright$. Sybolically, [[Universal Quantifier|for any]] $a, b, c \in S$, $\huge \begin{align} a \circ (b \triangleright c) &= (a\circ b) \triangleright (a \circ c) \\ (b\triangleright c)\circ a &=(b \circ a) \triangleright (c \circ a) \end{align} $