• A unordered collection of elements
  • Order and duplicates don’t matter


Set-Roster Notation

  • A Set may be specified by writing all of its elements between braces
  • Symbol is called ellipsis and read “and so forth”

Set-Builder Notation

  • The set of all x in U such that P(x) is true

Replacement Notation

  • For elements x in A, we apply the function t(x)


Membership of a Set

Cardinality of a Set

  • The size of the Set


Theorem 6.2.1

Inclusion of Intersection

Inclusion in Union

Transitive Property of Subsets

Set Identities


Set Equality

  • Second way to prove:

Ordered Pair

Order n-tuples

  • n denotes the number of Set we are multiplying
  • Ordered Pair is order 2-tuples, because are multiplying 2 sets

Cartesian Product

  • Thus
  • Cartesian Product of real numbers is basically a set that contains all the possible (x,y) coordinates on the Cartesian Plane
  • Depends on the number of set - n, the Cartesian product is a set of Order n-tuples