De Morgan's Law

Let $$\mathcal{A} = \{A_i : i \in I\}$$ be a collection of subsets of some set $$X$$ for some indexing set $$I$$. Then

$$\left(\bigcap_{i\in I} A_i\right)^c = \bigcup_{i \in I} A_i^c$$ and $$\left(\bigcup_{i\in I} A_i\right)^c = \bigcap_{i \in I} A_i^c$$