ROSTER FORM OF SET

Listing the elements of a set inside a pair of braces { } is called the roster form.

(i) Let A be the set of even natural numbers less than 11.

In roster form we write A = {2, 4, 6, 8, 10}

(ii) A = {x : x is an integer and- 1≤  x < 5}

In roster form we write A = {-1, 0,1, 2, 3, 4}

Solved Problems

Problem 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,...........}

Problem 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}

Problem 3 :

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

Solution :

A  =  {x : x is a natural number ≤ 8}

Roster form : 

A  =  {1, 2, 3, 4, 5, 6, 7, 8}

Problem 4 :

Write the following set in roster form :

A  =  {x : x ∈ N, 2 < x ≤ 10}

Solution :

A  =  {x : x ∈ N, 2 < x ≤ 10}

Roster form : 

A  =  { 3, 4, 5, 6, 7, 8, 9, 10}

Problem 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.

n = 1

x = 2n

x = 21

x = 2

n = 2

x = 2n

x = 22

x = 4

n = 3

x = 2n

x = 23

x = 8

n = 4

x = 2n

x = 24

x = 16

n = 5

x = 2n

x = 25

x = 32

Roster form :

X  =  {2, 4, 8, 16, 32}

Problem 6 :

Write the following set in roster form :

X  =  { x : x is a day in a week}

Solution :

X  =  { x : x is a day in a week}

Roster form :

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

Problem 7 :

Write the following set in roster form :

A  =  { x : x ,1/n, n ∈  N }

Solution :

A  =  { x : x ,1/n, n ∈  N }

Roster form : 

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

Problem 8 :

Write the following set in roster form :

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

Solution :

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

Roster form : 

A  =  {2, 4, 6, 8, .....................}

Problem 9 :

Write the following set in roster form :

The set of all whole numbers less than 10

Solution :

The set of all whole numbers less than 10

Roster form : 

A  =  {0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

Problem 10 :

Write the following set in roster form :

The set of all positive integers which are multiples of 3

Solution :

The set of all positive integers which are multiples of 3

Roster form :

{3, 6, 9, 12,.......................}

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