De_Morgan’s_Laws

Definition

$$ \left. (A \cap B) \right.^{c} = A^{c} \cup B^{c}, $$$$ \left. (A \cup B) \right.^{c} = A^{c} \cap B^{c} $$

This holds for arbitrarily many sets $A_{i} \subset X,i \in I$ ($I$ stands for an arbitrary index set),

$$ \left. \left( \bigcap(i \in I)A_{i} \right) \right.^{c} = \bigcup(i \in I)A_{i}^{c}, $$$$ \left. \left( \bigcup(i \in I)A_{i} \right) \right.^{c} = \bigcap(i \in I)A_{i}^{c}, $$