ROSTER FORM AND SET BUILDER NOTATION WORKSHEET

Question 1 :

List the elements of the following set in Roster form:

The set of all positive integers which are multiples of 7

Question 2 :

List the elements of the following set in Roster form:

The set of all prime numbers less than 20.

Question 3 :

Write the set A = { x : x is a natural number ≤ 8} in roster form.

Question 4 :

Write the following set in roster form

A = {x : x ∈ N, 2 < x ≤ 10}

Question 5 :

Write the following set in roster form

X =  {x : x = 2ⁿ, n ∈ N and n  ≤  5}

Question 6 :

Represent the following sets in set-builder form

X = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}

Question 7 :

Represent the following sets in set-builder form

A = {1, 1/2, 1/3, 1/4, ...............}

Question 8 :

Write the following sets in Set-Builder form

 The set of all positive even numbers

Question 9 :

Write the following sets in Set-Builder form

The set of all whole numbers less than 20

Question 10 :

Write the following sets in Set-Builder form

The set of all positive integers which are multiples of 3

Detailed Answer Key

Question 1 :

List the elements of the following set in Roster form:

The set of all positive integers which are multiples of 7

Solution : 

The set of all positive integers which are multiples of 7 in roster form is

{7, 14, 21, 28,...........}

Question 2 :

List the elements of the following set in Roster form:

The set of all prime numbers less than 20.

Solution : 

The set of all prime numbers less than 20 in roster form is

{2, 3, 5, 7, 11, 13, 17, 19}

Question 3 :

Write the set A = { x : x is a natural number ≤ 8} in roster form.

Solution :

A = { x : x is a natural number ≤ 8}.

So, the set contains the elements 1, 2, 3, 4, 5, 6, 7, 8.

Hence in roster form A = {1, 2, 3, 4, 5, 6, 7, 8}

Question 4 :

Write the following set in roster form

A = {x : x ∈ N, 2 < x ≤ 10}

Solution :

A = {x : x ∈ N, 2 < x ≤ 10}

Set A will contain elements greater than 2 and less than or equal to 10.

A = { 3, 4, 5, 6, 7, 8, 9, 10}

Question 5 :

Write the following set in roster form

X =  {x : x = 2ⁿ, n ∈ N and n  ≤  5}

Solution :

X =  {x : x = 2ⁿ, n ∈ N and n  ≤  5}

To find the elements in the given set, we need to apply the values 1, 2, 3, 4 ,5 respectively instead of n.

X = { 2, 4, 8, 16, 32}

Question 6 :

Represent the following sets in set-builder form

X = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}

Solution :

X = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}

The set X contains all the days of a week.

Hence in set builder form, we write

X = { x : x is a day in a week }

Question 7 :

Represent the following sets in set-builder form

A = {1, 1/2, 1/3, 1/4, ...............}

Solution :

A = {1, 1/2, 1/3, 1/4, ...............}

The denominators of the elements are 1, 2, 3, 4, ......

The set-builder form is A = { x : x ,1/n, n ∈  N }

Question 8 :

Write the following sets in Set-Builder form

 The set of all positive even numbers

Solution :

A = The set of all positive even numbers

The set-builder form is

A = { x : x is a positive even number}

Question 9 :

Write the following sets in Set-Builder form

The set of all whole numbers less than 20

Solution :

A = The set of all whole numbers less than 20

The set-builder form is

A = {x : x is a whole number and x < 20}

Question 10 :

Write the following sets in Set-Builder form

The set of all positive integers which are multiples of 3

Solution :

A = The set of all positive integers which are multiples of 3

The set-builder form is

A = {x : x is a positive integer and multiple of 3}

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