De Morgan laws ↩

Metadata

aliases: [De Morgan's theorem, De Morgan's laws, De Morgan law]

Theorem: For

and

sets the following are true:

In everyday words: complement of a set union equals the intersection of the complements of these sets. The same is true if we switch the union and intersection operations.

Proof

Omitted here, but can be proven in two parts by proving that the opposite sides are subsets of each other:

First prove that
Prove that