Complement laws

https://en.wikipedia.org/wiki/Complement_(set_theory)

Complement laws:

• A ⋃ Aᶜ = 𝓤

• A ⋂ Aᶜ = ∅

• 𝓤ᶜ = ∅ complement of the universal set is the empty set

• ∅ᶜ = 𝓤 complement of the empty set is the universal set

• A ⊆ B -> Bᶜ ⊆ Aᶜ

  follows from the equivalence of a conditional with its contrapositive, i.e. p -> q ≡ ¬q -> ¬p

• complement is like negation a ∨ ¬a = ⊤, a ∧ ¬a = ⊥