Sets and their Operations
Sets
Definition: For the purposes of this applet, any well defined collection of objects having common characteristics is going to be regarded as a set. Each object is known as member or element of the set.
Notation: Sets are usually denoted by capital letters , while their elements are denoted by lower case letters . If is an element of a set , then it is denoted as .
Definition: A set with no members is called empty set and it is denoted as or .
Definition: Two sets and are said to be equals if every member of belongs to and every member of belongs to .
Designating sets: Set-builder notation
The set is described by listing the properties that describe the elements of the set. Set-builder notation is comprised by two parts; namely:
- A variable , representing any elements of the set.
- A property which defines the elements of the set.
Designating sets: Listing method
In this method all of the member of the set are displayed, separated by commas.
Union of two sets
Definition: Let and be two sets. The union of and is the set whose members are elements of or .
Notation: The union of sets and is denoted as ; that is:
,
where symbol represents or.Intersection of two sets
Definition: Let and be two sets. The intersection of and is the set whose members are elements of and .
Notation: The intersection of sets and is denoted as ; that is:
,
where symbol represents and.Intersection and union of sets
Difference of two sets
Definition: Let and be two sets. The difference of and is the set whose members are elements of but they do not belong to .
Notation: The difference of sets and is denoted as ; that is:
.
Intersection and union of sets
Formative assessment
Use the following applet to practice finding the union, the intersection and the difference of the given sets.