NCERT Solutions for Class 11 Maths Chapter 1 Sets - FREE PDF Download
Class 11 Maths NCERT Solutions for Chapter 1 titled "Sets," lays the foundation for understanding one of the most fundamental concepts in mathematics. In this chapter, you'll learn about various types of sets, such as finite, infinite, equal, and null sets, along with crucial operations like union, intersection, and difference of sets.


It's essential to focus on understanding the notation and terminology used in sets, as these basics will be frequently used in higher mathematics. Pay special attention to Venn diagrams, as they provide a visual representation of set operations, making it easier to grasp complex concepts. This chapter is crucial, as it forms the basis for more advanced topics in mathematics. Access the latest Class 11 Maths Syllabus here.
Access Exercise Wise NCERT Solutions for Chapter 1 Maths Class 11
S.No. | Current Syllabus Exercises of Class 11 Maths Chapter 1 |
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6 | NCERT Solutions of Class 11 Maths Sets Miscellaneous Exercise |






Exercises Under NCERT Solutions for Class 11 Maths Chapter 1 Sets
NCERT Solutions for Class 11 Maths Chapter 1 "Sets" includes six exercises and a miscellaneous exercise. Here's a brief summary of each exercise:
Exercise 1.1: This exercise contains nine questions related to the basics of sets, including the definition of a set, the roster method, set-builder form, empty set, finite and infinite sets, equal sets, subsets, and the power set of a set.
Exercise 1.2: This exercise has seven questions based on set operations, such as the union, intersection, and complement of sets, and the properties of these operations, including the distributive law, commutative law, and associative law.
Exercise 1.3: This exercise covers Venn diagrams and their use in representing sets and solving problems related to sets, including questions on the union and intersection of sets, complement of sets, and solving word problems using Venn diagrams.
Exercise 1.4: This exercise includes eight questions related to the applications of sets in various fields, such as representing data using sets and sets in computer science, and includes questions related to the implementation of sets in programming.
Exercise 1.5: This exercise contains four questions based on the Cartesian product of sets, which is used to represent the ordered pairs of two sets, and applications of Cartesian products in mathematics.
Miscellaneous Exercise: This exercise contains ten questions of varying difficulty levels that cover a wide range of topics related to sets, including set theory, real-life applications of sets, and the properties of sets.
The exercises in NCERT Solutions for Class 11 Maths Chapter 1 Solutions are designed to help students build a strong foundation in the basics of sets and their applications in different fields. The solutions provided for each exercise include detailed explanations and step-by-step solutions to help students understand the concepts better.
Access NCERT Solutions for Class 11 Maths Chapter 1 – Sets
Exercise 1.1
1. Which of the following are sets? Justify your answer.
i. The collection of all months of a year beginning with the letter J.
Ans-
To determine if the given statement is a set
A set is a collection of well-defined objects.
We can definitely identify the collection of months beginning with a letter J.
Thus, the collection of all months of a year beginning with the letter J is the set.
ii. The collection of ten most talented writers of India
Ans-
To determine if the given statement is a set
A set is a collection of well-defined objects.
The criteria for identifying the collection of the ten most talented writers of India may vary from person to person. So it is not a well-defined object.
Thus, the collection of the ten most talented writers of India is not a set.
iii. A team of eleven best cricket batsmen in the world.
Ans-
To determine if the given statement is a set
A set is a collection of well-defined objects.
The criteria for determining the eleven best cricket batsmen may vary from person to person. So it is not a well-defined object.
Thus, a team of eleven best cricket batsmen in the world is not a set.
iv. The collection of all boys in your class.
Ans-
To determine if the given statement is a set
A set is a collection of well-defined objects.
We can definitely identify the boys who are all studying in the class. So it is a well-defined object.
Thus, the collection of all boys in your class is a set.
v. The collection of all-natural numbers is less than
Ans-
To determine if the given statement is a set
A set is a collection of well-defined objects.
We can identify the natural numbers less than
Thus, the collection of all-natural numbers less than
vi. A collection of novels written by the writer Munshi Prem Chand.
Ans-
To determine if the given statement is a set
A set is a collection of well-defined objects.
We can identify the books that belong to the writer Munshi Prem Chand. So it is a well-defined object.
Thus, a collection of novels written by the writer Munshi Prem Chand is a set.
vii. The collection of all even integers.
Ans-
To determine if the given statement is a set
A set is a collection of well-defined objects.
We can identify integers that are all the collection of even integers. So it is not a well-defined object.
Thus, the collection of all even integers is a set.
viii. The collection of questions in this chapter.
Ans-
To determine if the given statement is a set
A set is a collection of well-defined objects.
We can easily identify the questions that are in this chapter. So it is a well-defined object.
Thus, the collection of questions in this chapter is a set.
ix. A collection of the most dangerous animals in the world.
Ans-
To determine if the given statement is a set
A set is a collection of well-defined objects.
The criteria for determining the most dangerous animals may vary according to the person. So it is not a well-defined object.
Thus, the collection of the most dangerous animals in the world is a set.
2. Let
i.
Ans-
Given that,
To insert the appropriate symbol
The number
ii.
Ans-
Given that,
To insert the appropriate symbol
The number
iii.
Ans-
Given that,
To insert the appropriate symbol
The number
iv.
Ans-
Given that,
To insert the appropriate symbol
The number
v.
Ans-
Given that,
To insert the appropriate symbol
The number
vi.
Ans-
Given that,
To insert the appropriate symbol
The number
3. Write the following sets in roster form:
i.
Ans-
Given that,
To write the above expression in its roaster form
In roaster form, the order in which the elements are listed is immaterial.
The elements of the set are
ii.
Ans-
Given that,
To write the above expression in its roaster form
In roaster form, the order in which the elements are listed is immaterial.
The elements of the set are
iii.
Ans-
Given that,
To write the above expression in its roaster form
In roaster form, the order in which the elements are listed is immaterial.
The elements of the set are
iv.
Ans-
Given that,
To write the above expression in its roaster form
In roaster form, the order in which the elements are listed is immaterial.
The divisors of
The elements of the set are
v.
Ans-
Given that,
To write the above expression in its roaster form
In roaster form, the order in which the elements are listed is immaterial.
There are
The elements of the set are T, R, I G, O, N, M, E, Y.
vi.
Ans-
Given that,
To write the above expression in its roaster form
In roaster form, the order in which the elements are listed is immaterial.
There are
The elements of the set are B, E, T, R.
is
4. Write the following sets in the set builder form:
i.
Ans-
Given that,
To represent the given set in the set builder form
In set-builder form, all the elements of a set possess a single common property that is not possessed by any element outside the set.
From the given set, we observe that the numbers in the set are multiple of
ii.
Ans-
Given that,
To represent the given set in the set builder form
In set-builder form, all the elements of a set possess a single common property which is not possessed by any element outside the set.
From the given set, we observe that the numbers in the set are powers of
iii.
Ans-
Given that,
To represent the given set in the set builder form
In set builder form, all the elements of a set possess a single common property which is not possessed by any element outside the set.
From the given set, we observe that the numbers in the set are powers of
iv.
Ans-
Given that,
To represent the given set in the set builder form
In set builder form, all the elements of a set possess a single common property which is not possessed by any element outside the set.
From the given set, we observe that the numbers are the set of all even natural numbers.
v)
Ans-
Given that,
To represent the given set in the set builder form
In set builder form, all the elements of a set possess a single common property which is not possessed by any element outside the set.
From the given set, we observe that the numbers in the set squares of numbers form
5. List all the elements of the following sets:
i.
Ans-
Given that,
To list the elements of the given set
The odd natural numbers are
ii.
Ans-
Given that,
To list the elements of the given set
So the integers between
iii.
Ans-
Given that,
To list the elements of the given set
It is observed that,
iv.
Ans-
Given that,
To list the elements of the given set
There are
So the elements in the set are
v.
Ans-
Given that,
To list the elements of the given set
The months that don’t have
February, April, June, September, November
vi.
Ans-
Given that,
To list the elements of the given set
The consonants are letters in English alphabet other than vowels such as a, e, i, o, u and the consonants that precedes k include b, c, d, f, g, h, j
6. Match each of the sets on the left in the roaster form with the same set on the right described in set-builder form.
(i) {1, 2, 3, 6} | (a) {x : x is a prime number and a divisor of 6} |
(ii) {2, 3} | (b) {x : x is an odd natural number less than 10} |
(iii) {M,A,T,H,E,I,C,S} | (c) {x : x is natural number and divisor of 6} |
(iv) {1, 3, 5, 7, 9} | (d) {x : x is a letter of the word MATHEMATICS} |
i.
Ans-
Given that,
To match the roaster form in the left with the set builder form in the right
In roaster form, the order in which the elements are listed is immaterial.
In set builder form, all the elements of a set possess a single common property which is not possessed by any element outside the set.
It has been observed from the set that these set of numbers are the set of natural numbers which are also the divisors of
Thus,
ii.
Ans-
Given that,
To match the roaster form in the left with the set builder form in the right
In roaster form, the order in which the elements are listed is immaterial.
In set builder form, all the elements of a set possess a single common property which is not possessed by any element outside the set.
It has been observed from the set that these set of numbers are the set of prime numbers which are also the divisors of
Thus,
iii.
Ans-
Given that,
To match the roaster form in the left with the set builder form in the right
In roaster form, the order in which the elements are listed is immaterial.
In set builder form, all the elements of a set possess a single common property which is not possessed by any element outside the set.
It has been observed from the set of these letters of word MATHEMATICS.
Thus,
iv.
Ans-
Given that,
To match the roaster form in the left with the set builder form in the right
In roaster form, the order in which the elements are listed is immaterial.
In set builder form, all the elements of a set possess a single common property which is not possessed by any element outside the set.
It has been observed from the set that these sets of numbers are the set of odd numbers that are less than
Thus,
Exercise 1.2
1. Which of the following are examples of the null set
i. Set of odd natural numbers divisible by
Ans-
Given that,
Set of odd natural numbers divisible by
To find if the given statement is an example of null set
A set which does not contain any element is called the empty set or the null set or the void set.
There is no odd number that will be divisible by
ii. Set of even prime numbers
Ans-
Given that,
Set of even prime numbers.
To find if the given statement is an example of null set
A set which does not contain any element is called the empty set or the null set or the void set.
There was an even number
iii.
Ans-
Given that,
To find if the given statement is an example of null set
A set which does not contain any element is called the empty set or the null set or the void set.
There was no number that will be less than
iv.
Ans-
Given that,
To find if the given statement is an example of null set
A set which does not contain any element is called the empty set or the null set or the void set.
The parallel lines do not intersect each other. So it does not have a common point of intersection. So it is a null set.
2. Which of the following sets are finite or infinite.
i. The sets of months of a year
Ans-
Given that,
The sets of months of a year
To find if the set is finite or infinite
A set which is empty or consists of a definite number of elements is called finite otherwise the set is called infinite.
A year has twelve months which has defined number of elements
ii.
Ans-
Given that,
To find if the set is finite or infinite
A set which is empty or consists of a definite number of elements is called finite otherwise the set is called infinite.
The set consists of an infinite number of natural numbers.
iii.
Ans-
Given that,
To find if the set is finite or infinite
A set which is empty or consists of a definite number of elements is called finite otherwise the set is called infinite.
This set contains the elements from
iv. The set of positive integers greater than
Ans-
Given that,
The set of positive integers greater than
To find if the set is finite or infinite
A set which is empty or consists of a definite number of elements is called finite otherwise the set is called infinite.
The positive integers which are greater than
v. The set of prime numbers less than
Ans-
Given that,
The set of prime numbers less than
To find if the set is finite or infinite
A set which is empty or consists of a definite number of elements is called finite otherwise the set is called infinite.
The prime numbers less than
3. State whether each of the following set is finite or infinite:
i. The sets of lines which are parallel to
Ans-
Given that,
The set of lines which are parallel to
To find if the set is finite or infinite
A set which is empty or consists of a definite number of elements is called finite otherwise the set is called infinite.
The lines parallel to the
ii. The set of letters in English alphabet
Ans-
Given that,
The set of letter sin English alphabet
To find if the set is finite or infinite
A set which is empty or consists of a definite number of elements is called finite otherwise the set is called infinite.
English alphabet consist of
iii. The set of numbers which are multiple of
Ans-
Given that,
The set of numbers which are multiple of
To find if the set is finite or infinite
A set which is empty or consists of a definite number of elements is called finite otherwise the set is called infinite.
The numbers which are all multiple of
iv. The set of animals living on the earth
Ans-
Given that,
The set of animals living on the earth
To find if the set is finite or infinite
A set which is empty or consists of a definite number of elements is called finite otherwise the set is called infinite.
Although the number of animals on the earth is quite a big number, it is finite.
v. The set of circles passing through the origin
Ans-
Given that,
The set of circles passing through the origin
To find if the set is finite or infinite
A set which is empty or consists of a definite number of elements is called finite otherwise the set is called infinite.
The number of circles passing through the origin may be infinite in number.
4. In the following, state whether
i.
Ans-
Given that,
To state whether
We know that the order in which the elements are listed are insignificant. So
ii.
Ans-
Given that,
To state whether
We know that
iii.
Ans-
Given that,
To state whether
The positive integers less than
iv.
Ans-
Given that,
To state whether
The elements of A consists only of multiples of
5. Are the following pair of sets equal? Give reasons.
i.
Ans-
Given that,
To state whether
Solving
So
ii.
Ans-
Given that,
To state whether
We know that the order in which the elements are listed are insignificant. So
6. From the sets given below, select equal sets:
Ans-
Given that,
To select equal sets from the given set
Two sets A and B are said to be equal if they have exactly the same elements and we write A = B
We can observe from the sets that,
And thus
But
And checking other elements,
So
And thus,
And thus
And thus,
Similarly
We know that the order of the elements I listed are insignificant.
So
Exercise 1.3
1. Make correct statements by filling in the symbols
i.
Ans-
Given that,
To fill in the correct symbols
A set A is said to be a subset of B if every element of A is also an element of B
The element in the set
ii.
Ans-
Given that,
To fill in the correct symbols
A set A is said to be a subset of B if every element of A is also an element of B
The element in the set
iii.
Ans-
Given that,
To fill in the correct symbols
A set A is said to be a subset of B if every element of A is also an element of B
The set of students of class XI would also be inside the set of students in school
iv.
Ans-
Given that,
To fill in the correct symbols
A set A is said to be a subset of B if every element of A is also an element of B
The set of circles in the plane with a unit radius will be in the set of the circles in the same plane. So the set of circles in the plane is not in the set of circles with unit radius in the same plane.
v.
Ans-
Given that,
To fill in the correct symbols
A set A is said to be a subset of B if every element of A is also an element of B
From the given expression itself, we know that the set of triangles in the plane are not in the set of rectangles in the plane.
vi.
Ans-
Given that,
To fill in the correct symbols
A set A is said to be a subset of B if every element of A is also an element of B
From the above expression, we know that the set of equilateral triangles in the plane is in the set of triangles in the same plane
vii.
Ans-
Given that,
To fill in the correct symbols
A set A is said to be a subset of B if every element of A is also an element of B
The set of even natural numbers are in the set of integers.
2. Examine whether the following statements are true or false
i.
Ans-
Given that,
To examine whether the above statement is true or false
A set A is said to be a subset of B if every element of A is also an element of B
The element in the set
ii.
Ans-
Given that,
To examine whether the above statement is true or false
A set A is said to be a subset of B if every element of A is also an element of B
The element in the set
iii.
Ans-
Given that,
To examine whether the above statement is true or false
A set A is said to be a subset of B if every element of A is also an element of B
The element in the set
iv.
Ans-
Given that,
To examine whether the above statement is true or false
A set A is said to be a subset of B if every element of A is also an element of B
The element in the set
v.
Ans-
Given that,
To examine whether the above statement is true or false
A set A is said to be a subset of B if every element of A is also an element of B
The element in the set
vi.
Ans-
Given that,
A set A is said to be a subset of B if every element of A is also an element of B
3. Let
i.
Ans-
Given that,
To find if
A set A is said to be a subset of B if every element of A is also an element of B
From the above statement,
ii.
Ans-
Given that,
To find if
From the above statement,
iii.
Ans-
Given that,
To find if
A set A is said to be a subset of B if every element of A is also an element of B
From the above statement,
iv.
Ans-
Given that,
To find if
From the above statement,
v.
Ans-
Given that,
To find if
A set A is said to be a subset of B if every element of A is also an element of B
From the above statement,
An element of a set can never be a subset of itself. So
vi.
Ans-
Given that,
To find if
A set A is said to be a subset of B if every element of A is also an element of B
From the above statement,
The each element of
vii.
Ans-
Given that,
To find if
From the above statement,
Element of
So the given statement
viii.
Ans-
Given that,
To find if
A set A is said to be a subset of B if every element of A is also an element of B
From the above statement, we notice that,
ix.
Ans-
Given that,
To find if
A set A is said to be a subset of B if every element of A is also an element of B
From the above statement,
x.
Ans-
Given that,
To find if
A set A is said to be a subset of B if every element of A is also an element of B
From the above statement,
Since
xi.
Ans-
Given that,
To find if
A set A is said to be a subset of B if every element of A is also an element of B
From the above statement,
4. Write down all the subsets of the following sets:
i.
Ans-
Given that,
To write the subset of the given sets
A set A is said to be a subset of B if every element of A is also an element of B
Subsets of
ii.
Ans-
Given that,
To write the subset of the given sets
A set A is said to be a subset of B if every element of A is also an element of B
Subsets of
iii.
Ans-
Given that,
To write the subset of the given sets
A set A is said to be a subset of B if every element of A is also an element of B
Subsets of
iv.
Ans-
Given that,
To write the subset of the given sets
A set A is said to be a subset of B if every element of A is also an element of B
Subsets of
5. Write the following as intervals
i.
Ans-
Given that,
To write the above expression as intervals
The set of real numbers
ii.
Ans-
Given that,
To write the above expression as intervals
The set of real numbers
iii.
Ans-
Given that,
To write the above expression as intervals
The set of real numbers
iv.
Ans-
Given that,
To write the above expression as intervals
The set of real numbers
6. Write the following intervals in set builder form.
i.
Ans-
Given that,
To write the above interval in set builder form
The set of real numbers
ii.
Ans-
Given that,
To write the above interval in set builder form
The set of real numbers
iii.
Ans-
Given that,
To write the above interval in set builder form
The set of real numbers
iv.
Ans-
Given that,
To write the above interval in set builder form
The set of real numbers
7. What universal set(s) would you propose for each of the following:
i. The set of right triangles
Ans-
To propose the universal set for the set of right triangles
For the set of right triangles, the universal set can be the set of all kinds of triangles or the set of polygons.
ii. The set of isosceles triangles
Ans-
To propose the universal set for the set of right triangles
For the set of isosceles triangles, the universal set can be the set of all kinds of triangles or the set of polygons or the set of two dimensional figures.
8. Given the sets
i.
Ans-
Given that,
To find if the given set
It can be observed that,
ii.
Ans-
Given that,
To find if the given set
It can be observed that,
iii.
Ans-
Given that,
To find if the given set
It can be observe that,
iv.
Ans-
Given that,
To find if the given set
It can be observed that,
Exercise 1.4
1. Find the union of each of following pair of sets
i.
Ans-
Given that,
To find the union of two sets
Let A and B be any two sets. The union of A and B is the set which consists of all the elements of A and B.
ii.
Ans-
Given that,
To find the union of two sets
Let A and B be any two sets. The union of A and B is the set which consists of all the elements of A and B.
iii.
Ans-
Given that,
To find the union of two sets
Let A and B be any two sets. The union of A and B is the set which consists of all the elements of A and B.
iv.
Ans-
Given that,
To find the union of two sets
Let A and B be any two sets. The union of A and B is the set which consists of all the elements of A and B.
v.
Ans-
Given that,
To find the union of two sets
Let A and B be any two sets. The union of A and B is the set that consists of all the elements of A and B.
2. Let
Ans-
Given that,
To find if
A set A is said to be a subset of B if every element of A is also an element of B
It can be observed that
3. If A and B are two sets such that
Ans-
Given that,
A and B are two sets
To find
If A and B are two sets such that
4. If
i.
Ans-
Given that,
To find,
Let A and B be any two sets. The union of A and B is the set which consists of all the elements of A and B.
ii.
Ans-
Given that,
To find,
Let A and B be any two sets. The union of A and B is the set which consists of all the elements of A and B.
ii.
Ans-
Given that,
To find,
Let A and B be any two sets. The union of A and B is the set which consists of all the elements of A and B.
iii.
Ans-
Given that,
To find,
Let A and B be any two sets. The union of A and B is the set which consists of all the elements of A and B.
iv.
Ans-
Given that,
To find,
Let A and B be any two sets. The union of A and B is the set which consists of all the elements of A and B.
v.
Ans-
Given that,
To find,
Let A and B be any two sets. The union of A and B is the set which consists of all the elements of A and B.
vi.
Ans-
Given that,
To find,
Let A and B be any two sets. The union of A and B is the set which consists of all the elements of A and B.
5. Find the intersection of each pair of sets:
i.
Ans-
Given that,
To find the intersection of the given sets
The intersection of sets A and B is the set of all elements which are common to both A and B.
ii.
Ans-
Given that,
To find the intersection of the given sets
The intersection of sets A and B is the set of all elements which are common to both A and B.
iii.
Ans-
Given that,
To find the intersection of two sets
The intersection of sets A and B is the set of all elements which are common to both A and B.
iv.
Ans-
Given that,
To find the intersection of two sets
The intersection of sets A and B is the set of all elements which are common to both A and B.
v.
Ans-
Given that,
To find the intersection of two sets
The intersection of sets A and B is the set of all elements which are common to both A and B.
6. If
i.
Ans-
Given that,
To find,
The intersection of sets A and B is the set of all elements which are common to both A and B.
ii.
Ans-
Given that,
To find,
The intersection of sets A and B is the set of all elements which are common to both A and B.
iii.
Ans-
Given that,
To find,
The intersection of sets A and B is the set of all elements which are common to both A and B.
iv.
Ans-
Given that,
To find,
The intersection of sets A and B is the set of all elements which are common to both A and B.
v.
Ans-
Given that,
To find,
The intersection of sets A and B is the set of all elements which are common to both A and B.
vi.
Ans-
Given that,
To find,
The intersection of sets A and B is the set of all elements which are common to both A and B.
vii.
Ans-
Given that,
To find,
The intersection of sets A and B is the set of all elements which are common to both A and B.
viii.
Ans-
Given that,
To find,
The intersection of sets A and B is the set of all elements which are common to both A and B.
ix.
Ans-
Given that,
To find,
The intersection of sets A and B is the set of all elements which are common to both A and B.
x.
Ans-
Given that,
To find,
The intersection of sets A and B is the set of all elements which are common to both A and B.
7. If
i.
Ans-
Given that,
To find,
The intersection of sets A and B is the set of all elements which are common to both A and B.
ii.
Ans-
Given that,
To find,
The intersection of sets A and B is the set of all elements which are common to both A and B.
iii.
Ans-
Given that,
To find,
The intersection of sets A and B is the set of all elements which are common to both A and B.
iv.
Ans-
Given that,
To find,
The intersection of sets A and B is the set of all elements which are common to both A and B.
v.
Ans-
Given that,
To find,
The intersection of sets A and B is the set of all elements which are common to both A and B.
vi.
Ans-
Given that,
To find,
The intersection of sets A and B is the set of all elements which are common to both A and B.
8. Which of the following pairs of sets are disjoint
i.
Ans-
Given that,
To find if the given sets are disjoint
The difference between sets A and B in this order is the set of elements that belong to A but not to B.
Thus the element exists.
ii.
Ans-
Given that,
To find if the given sets are disjoint
The difference of the sets A and B in this order is the set of elements which belong to A but not to B.
Thus the element exists.
iii.
Ans-
Given that,
To find if the given sets are disjoint
The difference between sets A and B in this order is the set of elements that belong to A but not to B.
Thus the element does not exist.
9. If
i.
Ans-
Given that,
To find,
The difference of the sets A and B in this order is the set of elements which belong to A but not to B.
ii.
Ans-
Given that,
To find,
The difference of the sets A and B in this order is the set of elements which belong to A but not to B.
iii.
Ans-
Given that,
To find,
The difference of the sets A and B in this order is the set of elements which belong to A but not to B.
iv.
Ans-
Given that,
To find,
The difference of the sets A and B in this order is the set of elements which belong to A but not to B.
v.
Ans-
Given that,
To find,
The difference of the sets A and B in this order is the set of elements which belong to A but not to B.
vi.
Ans-
Given that,
To find,
The difference of the sets A and B in this order is the set of elements which belong to A but not to B.
vii.
Ans-
Given that,
To find,
The difference of the sets A and B in this order is the set of elements which belong to A but not to B.
viii.
Ans-
Given that,
To find,
The difference of the sets A and B in this order is the set of elements which belong to A but not to B.
ix.
Ans-
Given that,
To find,
The difference of the sets A and B in this order is the set of elements which belong to A but not to B.
x.
Ans-
Given that,
To find,
The difference of the sets A and B in this order is the set of elements which belong to A but not to B.
xi.
Ans-
Given that,
To find,
The difference of the sets A and B in this order is the set of elements which belong to A but not to B.
xii.
Ans-
Given that,
To find,
The difference of the sets A and B in this order is the set of elements which belong to A but not to B.
10. If
i.
Ans-
Given that,
To find,
The difference of the sets A and B in this order is the set of elements which belong to A but not to B.
ii.
Ans-
Given that,
To find,
The difference of the sets A and B in this order is the set of elements which belong to A but not to B.
iii.
Ans-
Given that,
To find,
The difference of the sets A and B in this order is the set of elements which belong to A but not to B.
11. If R is the real numbers and Q is the set of rational numbers, then what is
Ans-
Given that,
R is the real numbers
Q is the set of rational numbers
To find,
The difference of the sets A and B in this order is the set of elements which belong to A but not to B.
12. State whether each of the following statements is true or false. Justify your answer.
i.
Ans-
Given that,
To state whether the given statement is true
The difference of the sets A and B in this order is the set of elements which belong to A but not to B.
ii.
Ans-
Given that,
To state whether the given statement is true
The difference of the sets A and B in this order is the set of elements which belong to A but not to B.
iii.
Ans-
Given that,
To state whether the given statement is true
The difference of the sets A and B in this order is the set of elements which belong to A but not to B.
iv.
Ans-
Given that,
To state whether the given statement is true
Exercise 1.5
1. Let
i.
Ans-
Given that,
To find,
The complement of set A is the set of all elements of U which are not the elements of A.
ii.
Ans-
Given that,
To find,
The complement of set A is the set of all elements of U which are not the elements of A.
iii.
Ans-
Given that,
To find,
The complement of set A is the set of all elements of U which are not the elements of A.
iv.
Ans-
Given that,
To find,
The complement of set A is the set of all elements of U which are not the elements of A.
v.
Ans-
Given that,
To find,
The complement of set A is the set of all elements of U which are not the elements of A.
vi.
Ans-
Given that,
To find,
The complement of set A is the set of all elements of U which are not the elements of A.
2. If
i.
Ans-
Given that,
To find the complement of A
The complement of set A is the set of all elements of U which are not the elements of A.
ii.
Ans-
Given that,
To find the complement of B
The complement of set A is the set of all elements of U which are not the elements of A.
iii.
Ans-
Given that,
To find the complement of A
The complement of set A is the set of all elements of U which are not the elements of A.
iv.
Ans-
Given that,
To find the complement of A
The complement of set A is the set of all elements of U which are not the elements of A.
3. Taking the set of natural numbers as the universal set, write down the complements of the following sets:
i.
Ans-
Given that,
The set of natural number is the universal set
To find the complement of the set of even natural number
The complement of set A is the set of all elements of U which are not the elements of A.
ii.
Ans-
Given that,
The set of natural numbers is the universal set
To find the complement of the set of odd natural number
The complement of set A is the set of all elements of U which are not the elements of A.
iii.
Ans-
Given that,
The set of natural number is the universal set
To find the complement of the set of positive multiples of
The complement of set A is the set of all elements of U which are not the elements of A.
iv.
Ans-
Given that,
The set of natural number is the universal set
To find the complement of the set of prime number
The complement of set A is the set of all elements of U which are not the elements of A.
v.
Ans-
Given that,
The set of natural number is the universal set
To find the complement of the set of natural number divisible by
The complement of set A is the set of all elements of U which are not the elements of A.
vi.
Ans-
Given that,
The set of natural number is the universal set
To find the complement of the set of perfect squares.
The complement of set A is the set of all elements of U which are not the elements of A.
vii.
Ans-
Given that,
The set of natural number is the universal set
To find the complement of the set of perfect cube
The complement of set A is the set of all elements of U which are not the elements of A.
viii.
Ans-
Given that,
The set of natural number is the universal set
To find the complement of
The complement of set A is the set of all elements of U which are not the elements of A.
ix.
Ans-
Given that,
The set of natural number is the universal set
To find the complement of the
The complement of set A is the set of all elements of U which are not the elements of A.
x.
Ans-
Given that,
The set of natural number is the universal set
To find the complement of
The complement of set A is the set of all elements of U which are not the elements of A.
xi.
Ans-
Given that,
The set of natural number is the universal set
To find the complement of the
The complement of set A is the set of all elements of U which are not the elements of A.
4. If
i.
Ans-
Given that.
To prove that
Hence it has been proved that
ii.
Ans-
Given that.
To prove that
Hence it has been proved that
5. Draw appropriate Venn diagrams for each of the following:
i.
Ans-
To draw the Venn diagram for

ii.
Ans-
To draw the Venn diagram for

iii.
Ans-
To draw the Venn diagram for

iv.
Ans-
To draw the Venn diagram for

6. Let
Ans-
Given that,
To find
The complement of set A is the set of all elements of U which are not the elements of A.
7. Fill in the blanks to make each of the following a true statement:
i.
Ans-
To fill the blanks given in the statement
The union of the set and its complement is the universal set
ii.
Ans-
To fill the blanks given in the statement
We know that,
iii.
Ans-
To fill the blanks given in the statement
The intersection of the set and its complement is an empty set.
iv.
Ans-
To fill the blanks given in the statement
We know that,
Miscellaneous Exercise
1. Decide among the following sets, which sets are the subsets of one and another:
Ans-
Given that,
A set A is said to be a subset of B if every element of A is also an element of B
We can observe that,
2. In each of the following statements, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.
i. If
Ans-
To determine whether the statement is true
The given statement is false
For example,
Let
Now
But
Hence the given statement is false.
ii. If
Ans-
To determine whether the statement is true
The statement is false
For example,
Let
As
iii. If
Ans-
To determine whether the statement is true
The given statement is true.
Let
Let
iv. If
Ans-
To determine whether the statement is true
The given statement is false
Let
Now by the statement,
But
v. If
Ans-
To determine whether the statement is true
The given statement is false
Let
Now,
But
vi. If
Ans-
To determine whether the statement is true
The given statement is true
Let
To show that
Suppose
Then
3. Let
Ans-
To show that
Let
Case I:
Also
Similarly, we can show that
4. Show that the following four conditions are equivalent:
i.
ii.
iii.
iv.
Ans-
To show that the above four conditions are equivalent
First showing that,
(i)⬄(ii),
Let
To show,
If possible, suppose,
This means that there exist
Let
To show that,
Let
Let
To show
Clearly
Let
Case I:
So that
Case II:
Then
Conversely let
Let
Hence (i) ⬄ (iii)
Now we have to show that (i) ⬄ (iv)
Let
Let
We have to show that
As
Hence
Let
So that
Hence (i) ⬄ (iv)
5. Show that if
Ans-
Given that,
To show that,
Let
Hence it has been showed that
6. Show that for any sets
Ans-
To show that,
Let
We have to show that
Case I:
Then
Case II:
It is clear that,
From (1) and (2) we obtain that,
To prove that,
Let
(
Next we show that
Let
(
Hence from (3) and (4) we obtain that
Hence proved the statement
7. Using properties of sets, show that
i.
Ans-
To show that,
We know that,
And
From (1) and (2) we get that
Hence it has been showed that
ii.
Ans-
To show that
Hence it has been shown that
8. Show that
Ans-
Given that,
To show that the above does not imply
Let
Now,
But
9. Let
(Hints:
Ans-
Given that,
To show that,
We know that,
Now consider
It is possible only when
So from (1) and (2), we get,
10. Find sets
Ans-
Given that,
Let
Now,
And
Overview of Deleted Syllabus for CBSE Class 11 Maths Sets
Chapter | Dropped Topics |
Sets | Exercise 1.3 - Question 5 |
1.12 Practical Problems on Union and Intersection of Two Sets | |
Exercise 1.6 | |
Miscellaneous Exercise - Examples 31–34 and Question Number 6 and 7 | |
Miscellaneous Exercise - Question Number 13 - 16 | |
Summary - Last 5 Points |
Class 11 Maths Chapter 1: Exercises Breakdown
Exercise | Number of Questions |
Exercise 1.1 | 6 Questions & Solutions |
Exercise 1.2 | 6 Questions & Solutions |
Exercise 1.3 | 8 Questions & Solutions |
Exercise 1.4 | 12 Questions & Solutions |
Exercise 1.5 | 7 Questions & Solutions |
Miscellaneous Exercise | 10 Questions & Solutions |
Conclusion
NCERT Class 11 Math Chapter 1 on Sets provides a fundamental understanding of various types of sets, their representations, and operations, which are essential building blocks for higher mathematical concepts. This chapter covers critical topics such as the definition and types of sets, Venn diagrams, set operations, and their practical applications. Over the past few years, approximately 4-6 questions from Class 11 Maths Ch 1 were asked in exams, emphasizing its significance in the curriculum. A strong grasp of these concepts is vital for excelling in mathematics and preparing for more advanced topics in future studies.
Other Study Material for CBSE Class 11 Maths Chapter 1
S.No. | Important Links for Chapter 1 Sets |
1 | |
2 | |
3 | |
4 | |
5 | |
6 |
Chapter-Specific NCERT Solutions for Class 11 Maths
Given below are the chapter-wise NCERT Solutions for Class 11 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.
S. No | NCERT Solutions Class 11 Maths All Chapters |
1 | |
2 | |
3 | Chapter 4 - Complex Numbers and Quadratic Equations Solutions |
4 | |
5 | |
6 | |
7 | |
8 | |
9 | |
10 | Chapter 11 - Introduction to Three Dimensional Geometry Solutions |
11 | |
12 | |
13 |
Important Related Links for CBSE Class 11 Maths
S.No. | Important Study Material for Maths Class 11 |
1 | |
2 | |
3 | |
4 | |
5 | |
6 | |
7 | |
8 | |
9 | |
10 |
FAQs on NCERT Solutions for Class 11 Maths Chapter 1 Sets
1. What are the applications of Sets?
There are several applications of Sets in both mathematics and real life. Starting from formulating Calculus, Geometry and Topology to the formation of Algebra around rings, fields and groups. Plus, it also has various uses in fields like Chemistry, Physics, Biology, Computer Science and Electrical Engineering.
2. How many problems are there in each exercise of NCERT Solutions of Maths Class 11 Chapter 1?
Overall, there are six exercises along with a miscellaneous one. The number of questions for Ex. 1.1 is 6, Ex. 1.2 is 6, Ex. 1.3 is 9, Ex. 1.4 is 12, Ex. 1.5 is 7 and Ex. 1.6 is 8. Plus, the last exercise contains sixteen questions. You can easily get solutions to the problems in the form of PDF on web portals. Make sure to download them and refer to while preparing for your exam.
3. What topics are included in Class 11 Maths Chapter 1 Sets?
Class 11 Chapter 1 is Sets. It is generally referred to as concepts of relations and functions. It includes some of the fundamental operations and definitions that involve sets. This topic is counted as one of the simplest ones in the curriculum of Class 11, and students can score full marks in this section. With regards to the chapter topics, they comprise of Introduction, Sets and their Representations, The Empty Set, Infinite and Finite Sets, Equal Sets, Subsets, Power Sets, Universal Set, Venn Diagrams, Union of Sets, Operation on Sets, Intersection of Sets, Complement of a Set and practical problems on intersection and union of 2 separate Sets.
4. What are the basics of Class 11 Maths Chapter 1 - Sets?
Sets are used for defining functions and relations. The concept of Sets is covered in Chapter 1 of the Math NCERT textbook. This is considered an easy chapter, and you can score maximum marks in your exam. There are some basic definitions of the types of sets and a few formulas that you need to learn to become well-versed in this chapter. In Vedantu’s NCERT Solutions for Class 11 Maths, you will learn a way of solving these questions in an easy and quick way.
5. What are the real-time applications of Class 11 Maths Chapter 1 - Sets?
Sets are the foundation for several complex concepts. From the formulation of logical foundations for calculus, topology, and geometry to algebra related to the field, groups, and rings, Sets have a lot of applications in several fields of science and mathematics. This includes fields like physics, chemistry, biology, and electrical and computer engineering. You need to have a strong understanding of sets. For this, you can refer to Vedantu's NCERT Solutions for Class 11 Maths Chapter 1 - Sets.
6. What are the most important definitions that come in Class 11 Maths Chapter 1 - Sets?
Below are some of the most important definitions that you will be learning in Class 11 Maths Chapter 1 - Sets:
Empty Sets - An empty set is a set that has null elements or no elements.
Singleton Set - A set, which has one element is called a Singleton set.
Finite Set - A set with a finite number of elements is called a finite set.
Infinite Set - A set with an infinite number of elements is called an infinite set.
Equal Set - Two sets are said to be equal when every element of one set is also an element of the other set and vice versa.
7. What are the most important theorems that come in Class 11 Maths Chapter 1 - Sets?
Here are some important theorems that you will learn in Class 11 Maths Chapter 1 - Sets:
The union of two sets, A and B contain elements that are in set A and set B.
The intersection of sets A and B contain common elements from set A and B.
The complement of set A is the set of elements from the universal set U that are not in A.
These theorems will help you solve the questions related to Sets.
8. What are the most important formulas that I need to remember in Class 11 Maths Chapter 1 - Sets?
Here are some important formulas you need to remember from Class 11 Maths Chapter 1 - Sets:
If (A∪B)=ϕ, then n(A∪B)=n(A)+n(B)−n(A∩B)
If (A∩B)=ϕ, then n(A∪B)=n(A)+n(B)
(A∩B)′=A′∪B′
(A∪B)′=A′∩B′
You can find the solutions to these in Vedantu’s NCERT Solutions for Class 11 Maths Chapter 1- Sets on Vedantu (vedantu.com) free of cost. You can download the solutions from the Vedantu mobile app as well.
9. How can NCERT Solutions help in understanding Sets?
NCERT Solutions offer detailed, step-by-step explanations for each problem, enhancing students' grasp of set concepts and their practical applications. These solutions break down complex problems into manageable steps, making it easier to understand and apply the principles of sets.
10. Are these solutions beneficial for competitive exams?
Yes, the solutions are meticulously crafted by experts in accordance with NCERT guidelines, making them valuable for competitive exams like JEE and other entrance tests. They provide a solid foundation and practice for the types of questions encountered in these exams.

















