De Morgan's Laws

133. De Morgan’s Laws

Allows going back and forth between unions and intersections

133.1. Complement of a union

133.2. Complement of an intersection

133.3. Scaling

The general statement quantifies over an arbitrary index set:

{(⋃_{𝑛 \in 𝐼} 𝑆_{𝑛})}^{𝑐} = ⋂_{𝑛 \in 𝐼} 𝑆_{𝑛}^{𝑐} {(⋂_{𝑛 \in 𝐼} 𝑆_{𝑛})}^{𝑐} = ⋃_{𝑛 \in 𝐼} 𝑆_{𝑛}^{𝑐}

Two circles cannot show why $𝐼$ may be infinite, but two, three and four can show the direction of travel. Only the family changes below; the predicates are untouched.