- ∅
- ∅ ⊆ S if S is a set
- empty/nonempty
- finite/infinite
- T is finite if S is a finite set, T ⊆ S
- countable/uncountable
- countably infinite
- ∩
- (R ∩ S) ∩ T = R ∩ (S ∩ T) if U is a set, R, S, T ⊆ U
- S ∩ T = T ∩ S if U is a set, S, T ⊆ U
- S ∩ S = S if S is a set
- S ∩ T ⊆ S if U is a set, S, T ⊆ U
- S ∩ T ⊆ T if U is a set, S, T ⊆ U
- S ∩ ∅ = ∅ if S is a set
- ∅ ∩ S = ∅ if S is a set
- ∪
- (R ∪ S) ∪ T = R ∪ (S ∪ T) if U is a set, R, S, T ⊆ U
- S ∪ T = T ∪ S if U is a set, S, T ⊆ U
- S ∪ S = S if S is a set
- S ⊆ S ∪ T if U is a set, S, T ⊆ U
- T ⊆ S ∪ T if U is a set, S, T ⊆ U
- S ∪ ∅ = S if S is a set
- ∅ ∪ S = S if S is a set
- ∖
- S ⊎ T
- S × T
- P(S)
- maximal subset I of S such that pI
- Generalized operators
- Choice functions and axioms
- Multisets