Complement Union with Superset is Universe

Theorem

 * $S \subseteq T \iff \complement \left({S}\right) \cup T = \mathbb U$

where:
 * $S \subseteq T$ denotes that $S$ is a subset of $T$
 * $S \cup T$ denotes the union of $S$ and $T$
 * $\complement$ denotes set complement
 * $\mathbb U$ denotes the universal set.

Also see

 * Intersection with Complement is Empty iff Subset