De Morgan's Laws (Set Theory)/Set Complement/General Case

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Theorem

Let $\mathbb T$ be a set of sets, all of which are subsets of a universe $\mathbb U$.


Then:

Complement of Intersection

$\displaystyle \complement \paren {\bigcap \mathbb T} = \bigcup_{H \mathop \in \mathbb T} \complement \paren H$


Complement of Union

$\displaystyle \complement \paren {\bigcup \mathbb T} = \bigcap_{H \mathop \in \mathbb T} \complement \paren H$


Source of Name

This entry was named for Augustus De Morgan.