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

Theorem

Let $S$ be a set.

Let $\left\langle{S_i}\right\rangle_{i \in I}$ be a family of subsets of $S$.

Then:

Complement of Intersection

$\displaystyle \relcomp S {\bigcap_{i \mathop \in I} \mathbb S_i} = \bigcup_{i \mathop \in I} \relcomp S {S_i}$

Complement of Union

$\displaystyle \relcomp S {\bigcup_{i \mathop \in I} \mathbb S_i} = \bigcap_{i \mathop \in I} \relcomp S {S_i}$

Source of Name

This entry was named for Augustus De Morgan.