Definition of a Set:
A set is a well-defined collection of distinct objects, i.e. the nature of the object is the same, or in other words the objects in a set may be anything: numbers, people, places, letters, etc.
These objects are called the elements or members of the set.
A set is usually denoted by capital letters, i.e. etc., and the elements are denoted by small letters, i.e. etc.
If is any set and is the element of set , then we write , read as belongs to . If is any set and is not the element of set , then we write , read as does not belong to .
Representation of Sets:
There are three ways to represent a set.
I. Tabular Form:
Listing all the elements of a set, separated by commas and enclosed within curly brackets .
II. Descriptive Form:
State in words the elements of the set.
Set of first five natural numbers.
Set of positive even integers less than or equal to fifty.
Set of positive odd integers.
III. Set Builder Form:
Writing in symbolic form the common characteristics shared by all the elements of the set.
N = Natural numbers
E = Even numbers
O = Odd numbers