# 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

$\displaystyle \complement \paren {\bigcap \mathbb T} = \bigcup_{H \mathop \in \mathbb T} \complement \paren H$

#### Complement of Union

$\displaystyle \complement \paren {\bigcup \mathbb T} = \bigcap_{H \mathop \in \mathbb T} \complement \paren H$

## Source of Name

This entry was named for Augustus De Morgan.