Schröder Rule

Theorem
Let $A$, $B$ and $C$ be relations on a set $S$.

Then the following are equivalent statements:


 * $(1): \quad A \circ B \subseteq C$


 * $(2): \quad A^{-1} \circ \overline{C} \subseteq \overline{B}$


 * $(3): \quad \overline{C} \circ B^{-1} \subseteq \overline{A}$

where:
 * $\circ$ denotes relation composition
 * $A^{-1}$ denotes the inverse of $A$
 * $\overline{A}$ denotes the complement of $A$.

Also known as

 * This result is usually seen with "The" before it: The Schröder Rule.