In the Wolfram Language, sets are represented by sorted lists.

Union — find the union of any number of sets

Intersection — find the intersection of any number of sets

Complement — find the complement with respect to a universal set

SymmetricDifference — find the symmetric difference of any number of sets

Subsets — find all possible subsets of a set (the powerset)

Tuples — find all possible tuples of n elements from a set

Groupings — find all possible groupings of elements

Testing Relations between Sets

IntersectingQ  ▪  DisjointQ  ▪  SubsetQ

Testing Set Containment

ContainsAll  ▪  ContainsNone  ▪  ContainsAny  ▪  ContainsOnly  ▪  ContainsExactly

Testing Elements in Sets

Element  ▪  MemberQ  ▪  FreeQ

Operations on Subsets

SubsetCases — find subsets of elements matching a pattern

SubsetPosition  ▪  SubsetCount

SubsetReplace — replace subsets of elements

Constructing Sets from Lists

DeleteDuplicates  ▪  Sort  ▪  DuplicateFreeQ  ▪  DeleteAdjacentDuplicates  ▪  UniqueElements

Symbolic Set Theory

ForAll  ▪  Exists  ▪  Resolve