# Definition and Representation of Set

__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.

__Notation__**:**

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 .

**Example:**

**II. Descriptive Form:**

State in words the elements of the set.

**Example:**

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.

**Example:**

N = Natural numbers

E = Even numbers

O = Odd numbers