Sets

A mathematical set is a collection of distinct objects, such as numbers, letters, shapes, or functions. The objects in a set are called its elements or members. Sets can be defined by listing their elements between curly braces, or by using a rule or a description that specifies the criteria for membership.

The set {1, 2, 3} contains only the numbers 1, 2, and 3 as its elements.

The set {x : x²} contains square numbers as its elements.

Set Notation

 

Common Sets

 

Examples

List the sets defined by

 

Venn Diagrams

Venn diagrams are graphical representations of the relationships between sets of elements. U represents the Universal set

A U B : The union of sets A and B

The joining of sets A and B

 

A ∩ B The intersection of sets A and B

The elements that are in both A and B

 

 

A C B The complement of B ( aka B')

The elements not in set B

 

 

A - B The difference of A and B

The elements in Set A that are not in set B

 

 

Mutually exclusive : can't happen at same time

 

Not just two sets!

 

 

Functions

A function consists of two sets, the domain and codomain,
and a rule which maps each element of the domain
 to exactly one element in the codomain.

The Domain is the set of input numbers,
the Codomain is the set of possible output numbers,
the Range is the set of actual output images.

Example

so

Example

 

Example

 

Example