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