De Morgan's Laws (Set Theory)/Set Complement/Family of Sets

Theorem

Let $\left\langle{S_i}\right\rangle_{i \in I}$ be a family of sets, all of which are subsets of a universe $\mathbb U$.

Then:

Complement of Intersection

$\displaystyle \map \complement {\bigcap_{i \mathop \in I} S_i} = \bigcup_{i \mathop \in I} \map \complement {S_i}$

Complement of Union

$\displaystyle \map \complement {\bigcup_{i \mathop \in I} S_i} = \bigcap_{i \mathop \in I} \map \complement {S_i}$

Source of Name

This entry was named for Augustus De Morgan.