RD Sharma Solutions for Class 11 Maths Chapter 1 –
Sets
EXERCISE 1.1 PAGE NO: 1.2
1. What is the difference between a collection and a set? Give reasons to support
your answer.
Solution:
Well defined collections are sets.
Examples: The collection of good cricket players of India is not a set. However, the
collection of all good player is a set.
The collection of vowels in English alphabets is a set.
Thus, we can say that every set is a collection, but every collection is not necessarily a
set. Only well defined collections are sets.
2. Which of the following collections are sets? Justify your answer:
(i) A collection of all natural numbers less than 50.
(ii) The collection of good hockey players in India.
(iii) The collection of all the girls in your class.
(iv) The collection of all talented writers of India.
(v) The collection of difficult topics in Mathematics.
(vi) The collection of novels written by Munshi Prem Chand.
(vii) The collection of all questions of this chapter.
(viii) The collection of all months of a year beginning with the letter J.
(ix) A collection of most dangerous animals of the world.
(x) The collection of prime integers.
Solution:
(i) It is a set. Since, collection of all natural numbers less than 50 forms a set as it is well
defined.
(ii) It is not a set. Since, the term ‘good’ is not well defined.
(iii) It is a set. Since, a collection of all the girls in your class it is a definite quantity
hence it is a set.
(iv) It is not a set. Since, the term ‘most’ is not well defined. A writer may be talented in
the eye of one person, but he may not be talented in the eye of some other person.
(v) It is not a set. Since, the term ‘difficult’ is not well defined. A topic may be difficult
for one person, but may not be difficult for another person.
(vi) It is a set. Since, a collection of novels written by Munshi Prem Chand it is a definite
, RD Sharma Solutions for Class 11 Maths Chapter 1 –
Sets
quantity hence it is a set.
(vii) It is a set. Since, a collection of all the questions in this chapter. It is a definite
quantity hence it is a set.
(viii) It is a set. Since, a collection of all months of a year beginning with the letter J. It is
a definite quantity hence it is a set.
(ix) It is not a set. Since, the term ‘most dangerous’ is not well defined. The notion of
dangerous animals differs from person to person.
(x) It is a set. Since, a collection of prime integers. It is a definite quantity hence it is a
set.
3. If A={0,1,2,3,4,5,6,7,8,9,10}, then insert the appropriate symbol or in each of the
following blank spaces:
(i) 4 ……A
(ii) -4……A
(iii) 12…..A
(iv) 9…..A
(v) 0……A
(vi) -2……A
Solution:
The symbol ‘∈’ means belongs to. ‘∉’ means does not belong to.
(i) 4 ……A
4 ∈ A (since, 4 is present in set A)
(ii) -4……A
-4 ∉ A (since, -4 is not present in set A)
(iii) 12…..A
12 ∉ A (since, 12 is not present in set A)
(iv) 9…..A
9 ∈ A (since, 9 is present in set A)
(v) 0……A
0 ∈ A (since, 0 is present in set A)
, RD Sharma Solutions for Class 11 Maths Chapter 1 –
Sets
(vi) -2……A
-2 ∉ A (since, -2 is not present in set A)
, RD Sharma Solutions for Class 11 Maths Chapter 1 –
Sets
EXERCISE 1.2 PAGE NO: 1.6
1. Describe the following sets in Roster form:
(i) {x : x is a letter before e in the English alphabet}
(ii) {x ∈ N: x2 < 25}
(iii) {x ∈ N: x is a prime number, 10 < x < 20}
(iv) {x ∈ N: x = 2n, n ∈ N}
(v) {x ∈ R: x > x}
(vi) {x : x is a prime number which is a divisor of 60}
(vii) {x : x is a two digit number such that the sum of its digits is 8}
(viii) The set of all letters in the word ‘Trigonometry’
(ix) The set of all letters in the word ‘Better.’
Solution:
(i) {x : x is a letter before e in the English alphabet}
So, when we read whole sentence it becomes x is such that x is a letter before ‘e’ in the
English alphabet. Now letters before ‘e’ are a,b,c,d.
∴ Roster form will be {a,b,c,d}.
(ii) {x ∈ N: x2 < 25}
x ∈ N that implies x is a natural number.
x2 < 25
x < ±5
As x belongs to the natural number that means x < 5.
All numbers less than 5 are 1,2,3,4.
∴ Roster form will be {1,2,3,4}.
(iii) {x ∈ N: x is a prime number, 10 < x < 20}
X is a natural number and is between 10 and 20.
X is such that X is a prime number between 10 and 20.
Prime numbers between 10 and 20 are 11,13,17,19.
∴ Roster form will be {11,13,17,19}.
(iv) {x ∈ N: x = 2n, n ∈ N}
X is a natural number also x = 2n
∴ Roster form will be {2,4,6,8…..}.
This an infinite set.
(v) {x ∈ R: x > x}
Any real number is equal to its value it is neither less nor greater.
Sets
EXERCISE 1.1 PAGE NO: 1.2
1. What is the difference between a collection and a set? Give reasons to support
your answer.
Solution:
Well defined collections are sets.
Examples: The collection of good cricket players of India is not a set. However, the
collection of all good player is a set.
The collection of vowels in English alphabets is a set.
Thus, we can say that every set is a collection, but every collection is not necessarily a
set. Only well defined collections are sets.
2. Which of the following collections are sets? Justify your answer:
(i) A collection of all natural numbers less than 50.
(ii) The collection of good hockey players in India.
(iii) The collection of all the girls in your class.
(iv) The collection of all talented writers of India.
(v) The collection of difficult topics in Mathematics.
(vi) The collection of novels written by Munshi Prem Chand.
(vii) The collection of all questions of this chapter.
(viii) The collection of all months of a year beginning with the letter J.
(ix) A collection of most dangerous animals of the world.
(x) The collection of prime integers.
Solution:
(i) It is a set. Since, collection of all natural numbers less than 50 forms a set as it is well
defined.
(ii) It is not a set. Since, the term ‘good’ is not well defined.
(iii) It is a set. Since, a collection of all the girls in your class it is a definite quantity
hence it is a set.
(iv) It is not a set. Since, the term ‘most’ is not well defined. A writer may be talented in
the eye of one person, but he may not be talented in the eye of some other person.
(v) It is not a set. Since, the term ‘difficult’ is not well defined. A topic may be difficult
for one person, but may not be difficult for another person.
(vi) It is a set. Since, a collection of novels written by Munshi Prem Chand it is a definite
, RD Sharma Solutions for Class 11 Maths Chapter 1 –
Sets
quantity hence it is a set.
(vii) It is a set. Since, a collection of all the questions in this chapter. It is a definite
quantity hence it is a set.
(viii) It is a set. Since, a collection of all months of a year beginning with the letter J. It is
a definite quantity hence it is a set.
(ix) It is not a set. Since, the term ‘most dangerous’ is not well defined. The notion of
dangerous animals differs from person to person.
(x) It is a set. Since, a collection of prime integers. It is a definite quantity hence it is a
set.
3. If A={0,1,2,3,4,5,6,7,8,9,10}, then insert the appropriate symbol or in each of the
following blank spaces:
(i) 4 ……A
(ii) -4……A
(iii) 12…..A
(iv) 9…..A
(v) 0……A
(vi) -2……A
Solution:
The symbol ‘∈’ means belongs to. ‘∉’ means does not belong to.
(i) 4 ……A
4 ∈ A (since, 4 is present in set A)
(ii) -4……A
-4 ∉ A (since, -4 is not present in set A)
(iii) 12…..A
12 ∉ A (since, 12 is not present in set A)
(iv) 9…..A
9 ∈ A (since, 9 is present in set A)
(v) 0……A
0 ∈ A (since, 0 is present in set A)
, RD Sharma Solutions for Class 11 Maths Chapter 1 –
Sets
(vi) -2……A
-2 ∉ A (since, -2 is not present in set A)
, RD Sharma Solutions for Class 11 Maths Chapter 1 –
Sets
EXERCISE 1.2 PAGE NO: 1.6
1. Describe the following sets in Roster form:
(i) {x : x is a letter before e in the English alphabet}
(ii) {x ∈ N: x2 < 25}
(iii) {x ∈ N: x is a prime number, 10 < x < 20}
(iv) {x ∈ N: x = 2n, n ∈ N}
(v) {x ∈ R: x > x}
(vi) {x : x is a prime number which is a divisor of 60}
(vii) {x : x is a two digit number such that the sum of its digits is 8}
(viii) The set of all letters in the word ‘Trigonometry’
(ix) The set of all letters in the word ‘Better.’
Solution:
(i) {x : x is a letter before e in the English alphabet}
So, when we read whole sentence it becomes x is such that x is a letter before ‘e’ in the
English alphabet. Now letters before ‘e’ are a,b,c,d.
∴ Roster form will be {a,b,c,d}.
(ii) {x ∈ N: x2 < 25}
x ∈ N that implies x is a natural number.
x2 < 25
x < ±5
As x belongs to the natural number that means x < 5.
All numbers less than 5 are 1,2,3,4.
∴ Roster form will be {1,2,3,4}.
(iii) {x ∈ N: x is a prime number, 10 < x < 20}
X is a natural number and is between 10 and 20.
X is such that X is a prime number between 10 and 20.
Prime numbers between 10 and 20 are 11,13,17,19.
∴ Roster form will be {11,13,17,19}.
(iv) {x ∈ N: x = 2n, n ∈ N}
X is a natural number also x = 2n
∴ Roster form will be {2,4,6,8…..}.
This an infinite set.
(v) {x ∈ R: x > x}
Any real number is equal to its value it is neither less nor greater.
