Empty Intersection iff Subset of Complement

Theorem

 * $S \cap T = \varnothing \iff S \subseteq \complement \left({T}\right)$

where:
 * $S \cap T$ denotes the intersection of $S$ and $T$
 * $\varnothing$ denotes the empty set
 * $\complement$ denotes set complement
 * $\subseteq$ denotes subset.