**Roster form and set builder notation worksheet :**

Here we are going to see some practice problems on roster form and set builder notation.

(1) List the elements of the following set in Roster form:

The set of all positive integers which are multiples of 7

(2) List the elements of the following set in Roster form:

The set of all prime numbers less than 20.

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

(4) Write the following set in roster form

A = {x : x ∈ N, 2 < x ≤ 10}

(5) Write the following set in roster form

X = {x : x = 2^{n}, n ∈ N and n ≤ 5}

(6) Represent the following sets in set-builder form

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

(7) Represent the following sets in set-builder form

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

(8) Write the following sets in Set-Builder form

The set of all positive even numbers

(9) Write the following sets in Set-Builder form

The set of all whole numbers less than 20

(10) Write the following sets in Set-Builder form

The set of all positive integers which are multiples of 3

**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 = 2^{n}, n ∈ N and n ≤ 5}

**Solution :**

X = {x : x = 2^{n}, 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.

n = 1 x = 2 x = 2 x = 2 |
n = 2 x = 2 x = 2 x = 4 |
n = 3 x = 2 x = 2 x = 8 |
n = 4 x = 2 x = 2 x = 16 |
n = 5 x = 2 x = 2 x = 32 |

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}

After having gone through the stuff given above, we hope that the students would have understood "Roster form and set builder notation worksheet".

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