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}
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 = 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^{n} x = 2^{1} x = 2 |
n = 2 x = 2^{n} x = 2^{2} x = 4 |
n = 3 x = 2^{n} x = 2^{3} x = 8 |
n = 4 x = 2^{n} x = 2^{4} x = 16 |
n = 5 x = 2^{n} x = 2^{5} 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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