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:
 * $(1): \quad \displaystyle \complement \left({\bigcap_{i \mathop \in I} S_i}\right) = \bigcup_{i \mathop \in I} \complement \left({S_i}\right)$


 * $(2): \quad \displaystyle \complement \left({\bigcup_{i \mathop \in I} S_i}\right) = \bigcap_{i \mathop \in I} \complement \left({S_i}\right)$