Category:Schröder Rule

This category contains pages concerning Schröder Rule:

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

The following statements are equivalent:

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

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

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

where:

$\circ$ denotes relation composition

$A^{-1}$ denotes the inverse of $A$

$\overline A$ denotes the complement of $A$.