Sets

∅

empty set, {} ∅ ⊆ S (empty set is subset of everything)

∩

intersection

∈

is an element of

ℙ

power set set of all possible subsets of S |ℙ(S)| = 2^|S|

⊂

proper subset (can't be equals)

⊆

subset (every element of first set is in the second set)

∪

union

Cartesian Product

A × B set of all ordered pairs (a,b) where a ∈ A, b ∈ B

De Morgan's Laws

A ̅∪ ̅B ̅= A ̅∩ B ̅ A ̅∩ ̅B ̅= A ̅∪ B ̅

Complementation Laws

A ̿= A

Distributive Laws

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

Absorption Laws

A ∪ (A ∩ B) = A A ∩ (A ∪ B) = A

Associative Laws

A ∪ (B ∪ C) = (A ∪ B) ∪ C A ∩ (B ∩ C) = (A ∩ B) ∩ C

Idempotent Laws

A ∪ A = A A ∩ A = A

Complement Laws

A ∪ A ̅ = U A ∩ A ̅ = ∅

Commutative Laws

A ∪ B = B ∪ A A ∩ B = B ∩ A

Domination Laws

A ∪ U = U A ∩ ∅ = ∅

Identity Laws

A ∪ ∅ = A A ∩ U = A