# NCERT Solutions for Class 11 Maths Chapter 1 – Sets Free Download PDF

Sets Class 11 NCERT PDF material comes handy for all the students of Class 11. The solution material can be essential for last-minute revision. Download it and get accustomed to the critical techniques to solve questions related to Sets. The best part is that you can avail it free of cost. Every learner needs to get familiar with all the concepts of the chapter as it will help in studying other Maths topics like Probability, Sequences and Geometry. Although this is relatively an easy chapter, you still need to devote a considerable amount of time and practice for the same. Set Class 11 NCERT Solutions PDF by Vedantu is prepared for your assistance.

In NCERT Solutions for class 11 Maths Chapter 1 Sets, you will learn about the description of a Set, types of sets, subsets, concepts of subsets, Venn Diagrams, Operations on Sets using Venn Diagrams, Laws of Algebra of sets, some important results on number of elements in sets.

Free download NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.1, Ex 1.2, Ex 1.3, Ex 1.4, Ex 1.5, Ex 1.6 and Miscellaneous Exercise PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

## NCERT Solutions for Class 11 Maths Chapter 1 – Sets

### 11th Maths Chapter 1 Solutions

NCERT Solutions for Class 11 Maths Chapter 1 Sets in English Medium is given below to free download. These solutions and Offline apps 2021-22 are based on latest NCERT Books 2021-22 for all students who are following CBSE Syllabus 2021-22.

### Class 11 Maths Chapter 1 Solutions

The application of Sets lies in defining the concepts of relations and functions. Some of them are covered in this chapter. Ch 1 Maths Class 11 is categorised in different sections. Starting with the introductory part, it teaches you about Set. You can refer to the given examples to understand it better. Next, come the Sets and their representative topic which deals with the various types of sets. Here is an example of a problem from this section:

1. Write Down The Below-mentioned Sets in Set-builder Form:

a) {3, 6, 9, 12}
b) {2, 4, 8, 16, 32}
c) {5, 25, 125, 625}
d) {2, 4, 6, …..}
e) {1, 4, 9, ….., 100}

Sets Class 11 NCERT Solutions comprises Empty Sets, Finite and Infinite Sets, Sub Sets and Equal Sets. Furthermore, the Sub Set topic is divided into more sub-topics like intervals of subsets of R and a subset of a set of real numbers.

Examples of Questions:

1. Determine Which of The Following Sets Are Infinite or Finite

a) Set of alphabets in English
b) Set of animals on earth
c) Set of number which are multiples of 5

1. Which of The Following Sets Are Equal Sets? Find Out.

a) M = {2, 4, 8, 12}, N = {1, 2, 3, 4}, O = {4, 8, 12, 14}, P = {3, 1, 4, 2}
b) A = {-1, 1}, B = {0, a}, C = {1, -1}, D = {0, 1}

Sets Class 11 NCERT Solutions include Venn Diagram, Power Set, Universal Set and Operations. Again, the last topic is further categorised into union, difference and intersection of sets.

Question Examples:

1. What Will Be The Universal Set (S) For The Following?

a) A set of right angles
b) A set of scalene or isosceles triangle

1. Determine The Intersection of The Following Set Pairs.

a) A = {1, 3, 5}, B = {1, 2, 3}
b) X = {a, e, i, o, u}, Z = {a, b, c}

In Sets Class 11 NCERT Solutions, the final two topics of Sets are complements of a Set and real-life problems on intersection and union of sets.

Example of a Question From This Section:

1. Among a group of students, 50 of them know English, 100 of them know Hindi and 25 know both the languages and everyone knows either of the languages. How many students are there?

Together, all of these topics may seem a bit challenging at first, but you need not fret. Before proceeding with the exercises, you need to be thorough with all the concepts. As a reference, you can take help from online NCERT Solutions for Class 11 Maths Chapter 1 PDF and go through the same to know the tips and tricks to solve the sums.

## Why Should Students Download Class 11 Maths NCERT Solutions Chapter 1?

Following are the reasons why it is recommended to download Ch 1 Maths Class 11 PDF material:

Class 11 Sets solutions are written by scholars and rigorously follow the guidelines mandated by the CBSE Board.
The solutions are provided concisely, and step-by-step approach makes it easier for learners to comprehend.

Sometimes, due to lack of accurate reference materials, students find it challenging to understand and solve the problems. However, by making use of Sets Class 11 NCERT PDF presented by Vedantu, learners can stay assured to receive desired scores in exams.

## Important Questions On Sets

1. In a survey of 450 people, it was found that 110 play cricket, 160 play tennis and 70 play both cricket as well as tennis. How many play neither cricket nor tennis? [Answer: 23]
2. In a town of 10,000 families it was found that 40% families buy newspaper A, 20% families buy newspaper B and 10% families by newspaper C. 5% families buy A and B, 3%, buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, find the no of families which buy(1) A only (2) B only (3) none of A, B and C (4) exactly two newspapers (5) exactly one newspaper (6) A and C but not B (7) at least one of A,B, C. [Answer: {2, 3, 5}]
3. Two finite sets have m and n elements. The total number of subsets of first set is 56 more than the total number of subsets of the second set. Find the value of m and n. [Answer: m = 6 and n = 3]

## Class 11 Maths Chapter 1 Important Questions For Practice

1. In a group of 84 persons, each plays at least one game out of three viz. tennis, badminton and cricket. 28 of them play cricket, 40 play tennis and 48 play badminton. If 6 play both cricket and badminton and 4 play tennis and badminton and no one plays all the three games, find the number of persons who play cricket but not tennis.
2. In a class, 18 students took Physics, 23 students took Chemistry and 24 students took Mathematics of these 13 took both Chemistry and Mathematics, 12 took both Physics and Chemistry and 11 took both Physics and Mathematics. If 6 students offered all the three subjects, find: (1) The total number of students. (2) How many took Maths but not Chemistry. (3) How many took exactly one of the three subjects.

## How Many Exercises, Questions, And Examples Are There In Class 11 Maths Chapter 1?

• There are seven exercises in class 11 Maths Chapter 1 (Sets).
• In the first exercise (Ex 1.1), there are six questions.
• In the second exercise (Ex 1.2), there are six questions.
• In the third exercise (Ex 1.3), there are 9 questions.
• In the fourth exercise (Ex 1.4), there are 12 questions.
• In the fifth exercise (Ex 1.5), there are seven questions.
• In the sixth exercise (Ex 1.6), there are eight questions.
• In the last exercise (Miscellaneous), there are 16 questions.
• So, there are in all 64 questions in class 11 Maths Chapter 1.
• There are in all 34 examples in class 11 Maths Chapter 1.
• Examples 1, 2, 3, 4, 5 are in Ex 1.1.
• Examples 6, 7, 8 are in Ex 1.2.
• Examples 9, 10, 11 are in Ex 1.3.
• Examples 12, 13, 14, 15, 16, 17, 18, 19 are based on Ex 1.4.
• Examples 20, 21, 22 are in Ex 1.5.
• Examples 23, 24, 25, 26, 27 are in Ex 1.6.
• Examples 28, 29, 30, 31, 32, 33, 34 are based on Miscellaneous exercise.

## NCERT Solutions for Class 11 Maths Chapter 1 – Sets

How To Dunia provides all the concepts and solutions for Chapter 1 of Class 11 Maths in a creative and logical way. The PDF of Maths NCERT Solutions for Class 11 Chapter 1 includes the following topics and sub-topics.

1.1 Introduction

This section contains the origin, basic definition, and applications of sets.

1.2 Sets and their Representations

Here, students are able to know what a set is exactly and how it can be represented in roster/ set-builder and denoted using the English alphabets.

1.3 The Empty Set

This topic explains when a set is called an empty set.

1.4 Finite and Infinite Sets

Students can learn the definitions and examples of finite and infinite sets.

1.5 Equal Sets

This section gives an idea about equal and unequal sets along with solved examples.

1.6 Subsets

The main concepts covered under this section are:

• 1.6.1 Subsets of a set of real numbers
• 1.6.2 Intervals as subsets of R

1.7 Power Set

In this section, students are able to know the definition of power set, which has been derived from the concept of subsets.

1.8 Universal Set

This section is well explained with real-life examples such as population studies to define the universal set and representation using a letter.

1.9 Venn Diagrams

This section has the origin and definition of a Venn diagram. Also, it is explained using all the above topics and sub-topics.

1.10 Operations on Sets

We can perform some basic operations on sets similar to the addition or subtraction of numbers. These can be defined as below:

• 1.10.1 Union of sets
• 1.10.2 Intersection of sets
• 1.10.3 Difference of sets

1.11 Complement of a Set

After reading this section, students are able to understand the definition and properties of the complement of a set along with the examples as well as practice problems.

1.12 Practical Problems on Union and Intersection of Two Sets

Enough practise problems are provided under this section to help the students in order to understand in a better way about the union and intersection of two sets. These will help in their further studies to get thorough with the related concepts.

• Exercise 1.1 Solutions 6 Questions
• Exercise 1.2 Solutions 6 Questions
• Exercise 1.3 Solutions 9 Questions
• Exercise 1.4 Solutions 12 Questions
• Exercise 1.5 Solutions 7 Questions
• Exercise 1.6 Solutions 8 Questions

Miscellaneous Exercise On Chapter 1 Solutions 16 Questions

## Key Features of NCERT Solutions for Class 11 Maths Chapter 1- Sets

There are 6 exercises and a miscellaneous exercise in this chapter to help students understand the concepts related to Sets of the first term Class 11 Maths CBSE Syllabus (2021-22) in detail. The summary of the topics explained in Chapter 1 of NCERT Solutions for Class 11 Maths is listed below:

• A well-defined collection of objects is called a set.
• If a set does not contain any element, then it is called an empty set.
• Finite set: A set that consists of a definite number of elements
• Infinite set: A set that consists of an infinite number of elements
• Two sets A and B are said to be equal if they have the same elements.
• A set A is said to be a subset of a set B if every element of A is also an element of B. Intervals are subsets of R.
• A power set of a set A is a collection of all subsets of A. It is denoted by P(A).
• The union of two sets A and B is the set of all those elements which are either in A or B.
• The intersection of two sets A and B is the set of all elements which are common. The difference of two sets A and B in this order is the set of elements that belong to A but not to B.
• The complement of a subset A of universal set U is the set of all elements of U which are not the elements of A.
• For any two sets A and B, (A ∪ B)’ = A′ ∩ B′ and ( A ∩ B )′ = A′ ∪ B′.

## Frequently Asked Questions on NCERT Solutions for Class 11 Maths Chapter 1

What are the topics covered in Chapter 1 of NCERT Solutions for Class 11 Maths?

The topics covered in Chapter 1 of NCERT Solutions for Class 11 Maths are:

1. Introduction
2. Sets and their representations
3. The Empty Set
4. Finite and Infinite Sets
5. Equal Sets
6. Subsets
7. Power Set
8. Universal Set
9. Venn Diagrams
10. Operations on Sets
11. Complement of a Set
12. Practical problems on Union and Intersection of Two Sets

How many problems are there in each exercise of NCERT Solutions for Class 11 Maths Chapter 1?

Regular practice of the exercise wise problems helps students to understand the concepts covered in a better way. The number of questions in each exercise of Chapter 1 is as follows:

• Exercise 1.1 – 6 questions
• Exercise 1.2 – 6 questions
• Exercise 1.3 – 9 questions
• Exercise 1.4 – 12 questions
• Exercise 1.5 – 7 questions
• Exercise 1.6 – 8 questions
• Miscellaneous Exercise – 16 questions

What applications of Sets are discussed in Chapter 1 of NCERT Solutions for Class 11 Maths?

Sets have numerous applications in both real life and Mathematics. From formulating calculus, topology, geometry to the formation of algebra around fields, rings and groups, sets play a very important role. It is also used in other fields like Physics, Chemistry, Electrical Engineering, Computer Science and Biology.

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