PROP-DMG. De Morgan’s Laws (Set Theory).
For any $A$, $B\subseteq X$,
$X\smallsetminus A\cup B = (X\smallsetminus A)\cap(X\smallsetminus B)$;
$X\smallsetminus A\cap B = (X\smallsetminus A)\cup(X\smallsetminus B)$.
More generally, for any $A\subseteq\mathcal{P}(X)$,
$X\smallsetminus \bigcup A = \bigcap_{Y\in A}(X\smallsetminus Y)$;
$X\smallsetminus \bigcap A = \bigcup_{Y\in A}(X\smallsetminus Y)$.