What is the representation of sets in math?

 

A set can be represented in how many ways?

The three ways to represent a set in mathematics that are:

• Description Form
• Tabular Form
• Set Builder Form

Description Form:

A form of set that we have already studied in the introduction of sets is a statement form. So, we can define it as:

“When we write properties of set in a statement/sentenced form then it is called Descriptive form of sets.”

For Example

M = The set of books in a library

J = The sets of most popular cities in Pakistan

Q = The set of 5 bakery items 

Tabular Form:

This form of a set is also called roster form. We can define it as:

“When we write all elements in curly brackets and separate them by commas then this form of sets is called tabular form”.

For Example

N = The set of natural numbers from 6 to 8.

{6, 7, 8, 9, 10}

which is a tabular form

P = The set of prime numbers from 5 to 17

{5, 7, 11,13, 17}

which is a tabular form 

B = The set of 3 birds.

{crow, parrot, dove} which is a tabular form

K = The set of even numbers from 14 to 20

Set Builder Form:

In order to make a set well defined we write, a rule, a formula, or a statement within the curly brackets. Furthermore, every element of a set must have a single property to become an element of set in set builder form.

How to write sets in set-builder form?

The elements of sets are represented by symbols like

(x, y, z) etc. This variable is followed by a symbol colon ‘:’ or ‘|’ which is used to denote “such that” and after that, we write a description of elements in the set.  

For Example:

A = The set of family members 

{x:x are the family members} 

Or 

{x|x are the family members}

B = The set of odd numbers less than 7

{x:x ∊ O, x< 7}

C = The set of prime numbers between 3 and 7

{x:x ∊ P, 3<x<7}

Representation of sets in mathematics Practice Questions

Practice the following questions:

Question#1:

Write the following sets into the descriptive form.

 A = {2, 3, 5, 7, 9}

 B =  {books, notebooks, geometry box, pencil}

 C = {5,6,7,8,9,10} 

 D = { lion, fox, bear, elephant}

 E = {2, 4, 6, 8} 

 F = {brother, father, mother, sister}

G = {Imran khan, Nawaz Sharif, Ayyub Khan}

H = {hina, haram, Hafsa, hania} 

I = {0, ±1, ±2, ±3}

J = {Onion, ladyfinger, potato, brinjal}

Question#2

. Write the following sets into the tabular form.

 A = The set of vowels of the word 'Doctor'

B = The set of 2 bakery items.

 C = The set of 4 animals of jungle. 

 D = The set of 5 domestic animals.

 E = The set of 3 names of articles of stationery. 

 F = The set of 5 famous countries of the world. 

 G = The set of letters of the word 'medicine'. 

 I = The set of names of 4 girls whose names start with the letter “I”.

 J = The set of years greater than 2003 and less than 2007.

 K = The set of 3 food items.

Question#3

Write the following sets into the set-builder form. 

A = {pakora, biryani, Haleem, pasta, macaroni} 

 B = {0,1,2,...}

 C = {1, 4, 6, 8, 9, 10} 

 E = {7, 11, 13, 17, 19}

 F = {a, e, i, o, u}

 N = {1, 2, 3, 4,5}