De Morgan's Laws (Set Theory)/Set Complement/General Case

Theorem

Let $\mathbb T$ be a set of sets, all of which are subsets of a universe $\mathbb U$.

Then:

Complement of Intersection

$\ds \map \complement {\bigcap \mathbb T} = \bigcup_{H \mathop \in \mathbb T} \map \complement H$

Complement of Union

$\ds \map \complement {\bigcup \mathbb T} = \bigcap_{H \mathop \in \mathbb T} \map \complement H$

Source of Name

This entry was named for Augustus De Morgan.