Interested students can see the process of representation of sets on this page. We have three different ways to represent a set. Get the solved examples on sets in the following sections. Check out the Representation of a Set in set-builder form, roster form, and statement form from the below sections of this page. Also, refer to solved examples on the representation of a set using different notations explained clearly.
What is Meant by Representation of a Set?
Sets are the collection of well-defined objects. The numbers, alphabets and others enclosed between the curly braces of a set are called the elements. The elements are separated by a comma symbol. Usually, sets are denoted by capital letters i.e A, B, C and so on. We have three ways for representing a set, they are
1. Descriptive Form
2. Set Builder Form
3. Roster Form
Also, Read
Descriptive Form
It is a way of representing a set in the verbal statement. It gives a description of elements in the set. The description must allow a concise determination of which elements belong to the set and which elements do not.
Examples:
- The set of natural numbers less than 25.
- The set of vowels in the alphabets.
- The set of all letters in English alphabets.
- The set of prime numbers less than 50.
- The set of even numbers between 20 and 40.
Roster Form or Tabular Form
Roster form means listing all the elements of a set inside a pair of curly braces {}.
Examples:
The natural numbers less than 15 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14.
Let N be the set of natural numbers less than 15.
N = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}
The prime numbers lesser than 50 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
Let P be the set of prime numbers below 50.
P = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47}
Let M be the set of all months in a year.
Therefore, M = {January, February, March, April, May, June, July, August, September, October November, December}
Set-Builder Form or Rule Form
In the set-builder form, the statements are written inside a pair of braces. In this case, all the set elements must have a single property to become the set member. Here, the set elements are described by a symbol ‘x’ or any other variable followed by a colon “:” or slash “|”. After writing the symbol, you need to write a statement including the variable. In this, colon or slash stands for such that and braces stands for ‘set of all’.
Examples:
(i) Let P is the set of natural numbers between 15 and 25.
The set builder form is
P = { x : x is a natural number between 15 and 25 } or
P = { x | x is a natural number between 15 and 25 }
You can read this as P is a set of elements x such that x is a natural number between 15 and 25.
(ii) Let A denote the set of prime numbers between 5 and 50. It can be written in the set builder form as
A = { x | x is a prime number, 5 < x < 50 }
or A = { x : x ∈ P, 5 < x < 50 and P is an prime number }
(iii) The set B of all even natural numbers can be written as
B = {x : x is a natural number and x = 2n for n ∈ W}
Example Questions on Set Representation Using 3 Methods
Question 1:
The set of days of a week.
Solution:
Given that,
Set of days of a week.
The statement form is Set of seven days in a week.
The days in a week are Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday
The roster form is W ={Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}
The set-builder notation is W = { x : x is a day of the week }
Question 2:
The set of whole numbers lying between 5 and 25.
Solution:
Given that,
The set of whole numbers lying between 5 and 25.
The description notation is Set of whole numbers between 5 and 25.
The whole numbers lying between 5 and 25 are 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, and 24.
The set-builder form is A = {x | x is a whole number, 5 < x <24}
The roster form is A = {6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24}
Question 3:
The set of all numbers lesser than 16 and greater than 8.
Solution:
Given that,
The set of all numbers lesser than 16 and greater than 8.
The numbers greater than 8 and less than 16 are 9, 10, 11, 12, 13, 14, 15
The roster form is N = {9, 10, 11, 12, 13, 14, 15}
The statement form is the set of numbers between 8 and 16.
The set builder form is N = { x : x ∈ A, 8 < x < 16, A is a natural number}
FAQs on Representation of a Set
1. What are the ways for representing a set?
The 3 various ways of set representation are statement form or description form, set-builder form or rule form, roster form or tabular form.
2. What is the formula to use rule form?
The rule form formula is { x : property}. Here property defines the elements of a set.
3. What is the best way to represent sets?
According to me, the best and most used way of writing a set is roster form. The advantage of using the roster form is we can just list the set elements between the curly braces and each element is separated by a comma.
4. What are the two methods of writing sets?
The two main methods of representation of a set are using a Venn diagram or listing the elements (roster form). Venn diagram is the pictorial representation and roster form is the mathematical representation.