De Morgan's Laws (Set Theory)/Set Complement/Family of Sets
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Theorem
Let $\left\langle{S_i}\right\rangle_{i \in I}$ be a family of sets, all of which are subsets of a universe $\mathbb U$.
Then:
Complement of Intersection
- $\displaystyle \map \complement {\bigcap_{i \mathop \in I} S_i} = \bigcup_{i \mathop \in I} \map \complement {S_i}$
Complement of Union
- $\displaystyle \map \complement {\bigcup_{i \mathop \in I} S_i} = \bigcap_{i \mathop \in I} \map \complement {S_i}$
Source of Name
This entry was named for Augustus De Morgan.