# Definition and Representation of Set

__Definition____ ____of Set__**:**

Set is a well-defined collection of distinct objects (i.e. The nature of the object is the same or in other words object in a set may be anything: number, people, place, letters etc.)

These objects are called the elements or members of the sets.

__Notation__**:**

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 comma and enclosed within curly brackets .

**Example:**

**II. Descriptive Form:**

State in words the elements of sets.

**Example:**

Set of first five natural numbers.

Set of positive even integers less 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 sets.

**Example:**

N = natural numbers

E = Even numbers

O = Odd numbers