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:


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


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