De Morgan's Laws (Set Theory)/Proof by Induction
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Theorem
Let $\mathbb T = \left\{{T_i: i \mathop \in I}\right\}$, where each $T_i$ is a set and $I$ is some finite indexing set.
Then:
Difference with Intersection
- $\ds S \setminus \bigcap_{i \mathop \in I} T_i = \bigcup_{i \mathop \in I} \paren {S \setminus T_i}$
Difference with Union
- $\ds S \setminus \bigcup_{i \mathop \in I} T_i = \bigcap_{i \mathop \in I} \paren {S \setminus T_i}$
Source of Name
This entry was named for Augustus De Morgan.