Representation of a Set

Set is a well-defined collection of objects or elements. A Set is represented using the Capital Letters and the elements are enclosed within curly braces {}. Refer to the entire article to know about Representation of Set in three different ways such as Statement Form, Set Builder Form, Roster Form. For a Complete idea on this refer to the Set Theory and clear all your queries. Check out Solved Examples for all three forms explained step by step.

Sets can be represented in three different forms. Let us discuss each of them in detail by taking enough examples.

Statement Form or Descriptive Form
Roster or Tabular Form
Rule or Set Builder Form

Statement Form: In this Form, well-defined descriptions are provided for the elements or members in the set. Verbal Description of Elements is given. Statement Form is also known as Descriptive Form. Elements of the set are enclosed within curly brackets {}.

Example: Set of Odd Numbers Less than 10.

In Statement Form, the elements can be expressed as {1, 3, 5, 7, 9}

Set of Students in Class V having a height above 5 ft.

Set of Numbers greater than 30 and less than 40.

Roster Form: In the Roster Form elements of the set are represented within {} and are separated by commas. In this representation order of the elements doesn’t matter but the elements must not be repeated. Roster Form is also known as Tabular Form.

Example:

1. Set of Natural Numbers less than 10

Set of Natural Numbers Less than 10 = {1, 2, 3, 4, 5, 6, 7, 8, 9}

Set N in Roster Form is {1, 2, 3, 4, 5, 6, 7, 8, 9}

2. Set of Natural Numbers that divide 10

Y = { 1, 2, 5, 10}

3. W is the Set of Vowels in the Word Elephant

W = {E, A}

Kbps Full Form – Kilobits per second · kbps stands for kilobits per second.

Set Builder Form: In this form, all the elements possess a single property in order to be members of the set. In this representation of the set, the element is denoted by the symbol x or any variable followed by the symbol : or |. After this symbol write down the property possessed by the elements of the set and enclose the entire description within brackets.

Example:

1. Write the following Set in Set Builder Form = { 3, 6, 9, 12}

Set Builder Form is A = {x: x= multiples of 3, n ∈ N and n ≤ 15}

2. D = {x: x is an integer and – 2 < x < 11}

3. X = {m: m is a negative integer < -10}