# NCERT Solutions for Class 11 Maths Chapter 1 Sets (Ex 1.5)

One of India’s most recognised and highly esteemed educational bodies is the CBSE. There are schools associated with CBSE that are spread out over the nation. When it comes to educating its students, the CBSE board takes an impartial stance. The curriculum used by CBSE requires students to examine the subject and the ideas being taught in it in depth. The entire curriculum is developed by CBSE with the goal of ensuring that all of its students comprehend the complex ideas taught at the upper secondary level. In addition to encouraging students to think critically and analytically, CBSE encourages them to look at subjects outside of the box. Students’ understanding of the concepts from the curriculum must be so complete that they can quickly visualise all the fundamentals they were taught. It is emphasised to students that regular recapitulation and active recall are more important than memorisation. Students are well aware of CBSE’s extensive syllabus. Students must therefore be able to sort through the knowledge that is redundant and not needed for the exams. Teachers at Extramarks have expressed empathy for the kids’ struggles and have given helpful strategies for overcoming them. Every student has been informed by teachers that there is nothing to be concerned about with the CBSE curriculum. Teachers encourage their students to take their studies seriously and to make small adjustments to their daily routines.

The National Council of Educational Research and Training (NCERT) is a centralised managed organisation. In 1961, the Indian government founded NCERT. NCERT assists the Indian Government in making decisions on the nation’s educational system. In order to make choices regarding all issues pertaining to the country’s educational growth, NCERT offers assistance to both the Central Government and the State Governments. NCERT and CBSE have a very synergistic connection in which they collaborate closely. NCERT offers their own set of principles and regulations. If students want to perform well on the tests, students must adhere to the norms and guidelines that have been set forth.

NCERT books are considered essential books for CBSE students, and their benefits will help build the foundation for academic examinations or competitive examinations. NCERT books are very helpful for students as they build a strong base for them and enhance their knowledge. NCERT books are more than enough to cover and develop the understanding of basic fundamentals in every subject in an easy language. An important fact of NCERT books is that students get their concepts clear by just going through NCERT books. Students must focus on understanding concepts rather than just memorising them. When students understand the topics, then they will be easily able to solve any question concerning that very concept. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 will help the students to understand even the complex and complicated topics of the given chapter. With the help of the Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5, students will be able to solve the difficult questions of that exercise. Mathematics may seem like a complex subject for students, but NCERT books have been designed in easy and understanding language. After studying from NCERT books, students may not understand NCERT exercise questions at times, then Extramarks’ website provides them with the easiest and most understanding solution to solve the questions of the NCERT textbook by downloading Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5.

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## NCERT Solutions for Class 11 Maths Chapter 1 Sets (Ex 1.5) Exercise 1.5

CBSE students of Class 11 can easily download solutions of Maths 1.5 Class 11. They can download the Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 from Extramarks’ website or mobile application in PDF format so that they can study Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 even in offline mode.

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### Access NCERT Solutions for Class 11 Mathematics Chapter 1 – Sets

Students can get access to the NCERT Solutions for Class 11 Mathematics Chapter 1- Sets from Extramarks’ website or mobile application and they can download the answers from Extramarks in PDF format so that they can use the answers even in offline mode when they would not be connected to the internet.

There are a total of 7 questions in the Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5,and each question has been solved in the easiest method by the experts in Mathematics. There are a total of six exercises, and at the end of chapter 1, there are 16 questions of miscellaneous exercises.

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### Class 11 Maths NCERT Solutions Chapter 1 – An Overview of Sets

Every chapter in Class 11 must be covered with meticulous planning and distinctive strategies. There are seven exercises in Chapter 1 and one miscellaneous exercise. Each of them contains questions based on theories and formulas presented in Chapter 1 of the NCERT Mathematics textbook for Class 11. While textbook solutions are helpful when completing these exercises, students may encounter difficulties with certain questions. In that case, students can go to the Extramarks’ website and download detailed and step-by-step solutions to all of the questions in the Exercise. Students should download the Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 to get detailed solutions and cover Class 11 Maths Chapter 1 Exercise 1.5. The Extramarks solutions are of the highest quality.

Chapter 1 is very easy if the student is studying properly. Every Chapter of Class 11 has an important role if a student is planning to appear in the Joint Entrance Exam (JEE). The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 has provided every important formula that is needed to solve questions. The different elements of a Set are generally described by a capital letter. Thus, A is the set, and 1, 2, 3, 4, and 5 are the set’s elements or members. The Set’s elements can be written in any order but cannot be repeated. In the case of alphabets, all of the elements of the Set are represented in small letters. We can also write it as 1 A, 2 A, and so on. The set’s cardinal number is 5. The following are some examples of commonly used sets:

N: the set of all-natural numbers.

Z: Set of all integers

Q: the set of all rational numbers

R: the set of all real numbers.

Z+: the set of all positive integers.

This chapter is a building foundation for the development of students, and that foundation will be strong with the support of the Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5. Those students who will stay focused on their studies from the very beginning will score better in their examinations and even do well in their competitive examinations, like JEE or CUET.

This chapter builds the basic understanding of Sets and questions in JEE also arise from this. Though the chapter is not that complex, its application could be tough at times. Just mugging up NCERT Solutions will not help students in the long run. Therefore, they must understand the concepts and know the application of each concept because Mathematics is all about concepts and practice.

Then another topic that has been mentioned in the Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5, the order of a set determines how many elements it contains. It describes the size of a set. The order of the set is also known as cardinality. The size of a set, whether finite or infinite, is referred to as a set of finite or infinite order.

Initially, students must practice Sets topic-wise only and then go ahead. Students must not rush into things that will cause them confusion in the future when they appear in their examinations. So, to understand certain topics and chapters Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 is always there to help students. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 are a safe tool for students as it covers each question of the exercise and that will eventually make the work of students easier.

The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 gives an explanation of the types of Sets. There are several types of sets in Mathematics- Empty Sets, Singleton Sets, Finite Sets, Infinite Sets, Equivalent Sets, Equal Sets, Disjoint Sets, Subsets, Proper Subsets, Supersets, and Universal Sets. After understanding the concepts, students must practice them themselves to understand them properly. Each one of the topics has been discussed in Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5.

The Chapter after Sets is interrelated to each other. Therefore, to understand the next chapter of the NCERT Mathematics book students must focus from the very beginning of the chapter and study topic-wise.

### NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.5 – All Questions

Students can download NCERT Solutions in English and Hindi Medium for Class 11 Maths Chapter 1 Sets Ex 1.5 in PDF format. The Maths Class 11 Exercise 1.5 is solved by experienced experts from Extramarks who produced these NCERT solutions. All the questions in Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 have thorough explanations from the NCERT Textbook. Not only Ex 1.5 but all other exercises from Chapter 1 are available in NCERT Solutions for Class 11 Maths Chapter 1. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 were created with the help of competent topic specialists, which increases their dependability and accuracy. The NCERT Solutions Class 11 Maths Chapter 1 Exercise 1.5 are available in PDF format for offline access.There are a total of seven questions in the exercise -1.5 and each of them is solved from the point of view of getting step marking. Hence, the students should never try to memorise the questions but rather try to understand them. Even if the students find something complex while studying,they should read it again and again until they understand the whole concept. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 are solved with the easiest step and in the easiest language. Students are advised to do their work honestly so that they will not suffer in their examinations.

### Extramarks – The Best Place to Get Your Doubts Cleared

Extramarks is a learning platform specially designed for students who rely on NCERT books. Extramarks is a platform where specific subject experts such as educators, make solutions for the NCERT books. Then they make sample paper questions for students to revise and retain the topics they have already read. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5, give clarity to the students, and they will be able to solve any question. So, to download Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5, students should go to Extramarks’ website and mobile application, which will be easily available in PDF format.

Apart from the Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5, students can also access other study materials like live classes, past years’ papers, sample papers, complete syllabus etc.

The Extramarks’ website or mobile application is very reliable to students as it makes answers and sample questions with accuracy so that no issue arises for the students who are preparing for JEE or other competitive exams. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5, will make sure that no problem will occur to students in the time of their need. If students will prepare minutely and practice Mathematics rigorously, then they can compete in any examination and do well.

Extramarks is always there for students to improve their skills. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 will improve their skills in answering questions. Students are indeed already-intelligent but Extramarks brushes them up and makes them understand the Chapter in a vivid and specific manner. Extramarks makes its own questions for students to practice over. It will be quite evident to students that they can understand the topics and chapters better when they get help from Extramarks and practice them.

Every chapter of Class 11 solutions has been solved by Extramarks experts, students can also search for others chapters as well.

NCERT Solutions Class 11 Chapter 2 – Relations and Functions

NCERT Solutions Class 11 Chapter 3- Trigonometric Functions

NCERT Solutions Class 11 Chapter 4- Principle of Mathematical Induction

NCERT Solutions Class 11 Chapter 5- Complex Numbers and Quadratic Equations

NCERT Solutions Class 11 Chapter 6- Linear Inequalities

NCERT Solutions Class 11 Chapter 7- Permutations and Combinations

NCERT Solutions Class 11 Chapter 8- Binomial Theorem

NCERT Solutions Class 11 Chapter 9- Sequences and Series

NCERT Solutions Class 11 Chapter 10- Straight Lines

NCERT Solutions Class 11 Chapter 11- Conic Sections

NCERT Solutions Class 11 Chapter 12- Introduction to Three Dimensional Geometry

NCERT Solutions Class 11 Chapter 13- Limits and Derivatives

NCERT Solutions Class 11 Chapter 14- Mathematical Reasoning

NCERT Solutions Class 11 Chapter 15- Statistics

NCERT Solutions Class 11 Chapter 16- Probability

Students can also download NCERT Solutions for other classes by clicking the links given below-

Ncert Solutions Class 11

Ncert Solutions Class 10

Ncert Solutions Class 9

Ncert Solutions Class 8

Ncert Solutions Class 7

Ncert Solutions Class 6

Ncert Solutions Class 5

Ncert Solutions Class 4

Ncert Solutions Class 3

Ncert Solutions Class 2

Ncert Solutions Class 1

**Q.1 ** Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9},

A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find

(i) A′

(ii) B′

(iii) (A ∪ C)′

(iv) (A ∪ B)′

(v) (A′)′

(vi) (B – C)’

**Ans.**

(i) A’ = U – A = {5, 6, 7, 8, 9}

(ii) B’ = U – B = {1, 3, 5, 7, 9}

(iii) A ∪ C = {1, 2, 3, 4, 5, 6}

(A ∪ C)’ = U – (A ∪ C)

= {7, 8, 9}

(iv) A ∪ B = {1, 2, 3, 4, 6, 8}

(A ∪ B)’ = U – (A∪B)

= {5, 7, 9}

(v) (A’)’ = U – (A’)

= {1, 2, 3, 4}

(vi) B – C = {2, 8}

(B – C)’ = U – (B – C)

= {1, 3, 4, 5, 6, 7, 9}

**Q.2 ** If U = {a, b, c, d, e, f, g, h}, find the complements of the following sets:

(i) A = {a, b, c}

(ii) B = {d, e, f, g}

(iii) C = {a, c, e, g}

(iv) D = {f, g, h, a}

**Ans.**

(i) A = {a, b, c}

A’ = U – A

= {d, e, f, g, h}

(ii) B = {d, e, f, g}

B’ = U – B

= {a, b, c, h}

(iii) C = {a, c, e, g}

C’ = U – C

= {b, d, f, h}

(iv) D = {f, g, h, a}

D’ = U – D

= {b, c, d, e}

**Q.3** Taking the set of natural numbers as the universal set, write down the complements of the following sets:

(i) {x: x is an even natural number}

(ii) {x: x is an odd natural number}

(iii) {x: x is a positive multiple of 3}

(iv) {x: x is a prime number}

(v) {x: x is a natural number divisible by 3 and 5}

(vi) {x: x is a perfect square}

(vii) {x: x is a perfect cube}

(viii) {x: x + 5 = 8}

(ix) {x: 2x + 5 = 9}

(x) { x : x ≥ 7 }

(xi) { x : x ∈ N and 2x + 1 > 10 }

**Ans.**

Here, U = N = {1, 2, 3, 4, 5, …}

(i) Let A = {x: x is an even natural number}

A’ = U – A

= {1, 3, 5, 7, …}

= {x: x is an odd natural number}

(ii) Let B = {x: x is an odd natural number}

B’ = U – B

= {2, 4, 6, 8, …}

= {x : x is an even natural number}

(iii) Let C = {x: x is a positive multiple of 3}

C’ = U – C

= {1, 3, 4, 5, 7, …}

= {x : x is a natural number but not a multiple of 3}

(iv) Let D = {x: x is a prime number}

D’ = U – D

= {x : x is composite number and 1}

(v) Let E = {x: x is a natural number divisible by 3 and 5}

E’ = U – E

= {x: x is a natural number neither divisible by 3 nor by 5}

(vi) Let F = {x: x is a perfect square}

F’ = U – F

= {x : x is not a perfect square}

(vii) Let G = {x: x is a perfect cube}

G’ = U – G

= {x : x is not a perfect cube}

(viii) Let H = {x: x + 5 = 8}

= {3}

H’ = U – H

= {x : x is a natural number except 3}

(ix) Let I = {x: 2x + 5 = 9}

= {2}

I’ = U – I

= {x : x is a natural number except 2}

(x) Let J = { x:x ≥ 7}

J’ = U – J

= {1, 2, 3, 4, 5, 6}

(xi) Let K = {x : x ∈ N and 2x + 1 > 10}

= { x : x ∈ N and x > 9/2}

= {5, 6, 7, 8, …}

K’ = U – K

= {1, 2, 3, 4}

**Q.4 ** If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that

(i) (A ∪ B)′ = A′ ∩ B′

(ii) (A ∩ B)′ = A′ ∪ B′

**Ans.**

A ∪ B = {2, 3, 4, 5, 6, 7, 8}

A ∩ B = {2}

(i) L.H.S.:

(A ∪ B)′ = U – (A ∪ B)

= {1, 9}

R.H.S.:

A′ ∩ B′ =(U – A) ∩ ( U – B)

= {1, 3, 5, 7, 9}∩{1, 4, 6, 8, 9}

= {1, 9}

Thus,

(A ∪ B)′ = A′ ∩ B′

(ii) L.H.S.:

(A ∩ B)′ = U – (A ∩ B)

= {1, 3, 4, 5, 6, 7, 8, 9}

R.H.S.:

A′ ∪ B′=(U – A) ∪ ( U – B)

= {1, 3, 5, 7, 9} ∪ {1, 4, 6, 8, 9}

= {1, 3, 4, 5, 6, 7, 8, 9}

Thus,

(A ∩ B)’ = A′ ∪ B′

**Q.5 ** Draw appropriate Venn diagram for each of the following :

(i) (A ∪ B)’, (ii) A′ ∩ B′,

(iii) (A ∩ B)′, (iv) A′ ∪ B′

**Ans.**

(i) (A ∪ B)’

(ii) A′ ∩ B′=(A ∪ B)’ [By De Morgan’s Law]

(iii) (A ∩ B)′

(iv) A′ ∪ B′ = (A ∩ B)′ [By De Morgan’s Law]

**Q.6 ** Let U be the set of all triangles in a plane. If A is the set of all triangles with at least one angle different from 60°, what is A′?

**Ans.**

Here, U = set of all triangles in a plane,

A = set of all triangles with at least one angle different from 60°

A’ = set of all triangles with each angle 60° i.e., set of all equilateral triangles.

**Q.7 ** Fill in the blanks to make each of the following a true statement:

(i) A ∪ A′ = . . .

(ii) Φ′ ∩ A = . . .

(iii) A ∩ A′ = . . .

(iv) U′ ∩ A = . . .

**Ans.**

(i) A ∪ A′ = __U__

(ii) Φ′ ∩ A = __A__

(iii) A ∩ A′ = __Φ__

(iv) U′ ∩ A = __Φ__

## FAQs (Frequently Asked Questions)

### 1. How can students access the Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5?

Students can get the Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 from the website of Extramarks and mobile application of the same and download the PDF format from there only. These solutions are easy to understand and helpful for students concerning their board examinations and other entrance tests.

### 2. Is it helpful to download the Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5?

Yes, undoubtedly it is very helpful to download the Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 because they are topic-wise notes and solutions to NCERT questions. Notes are also given with these solutions so that students do not have to worry about anything. They just have to focus on studying minutely and in the end, they will be able to solve all their issues.

### 3. Are the Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 in accordance with the updated syllabus of Maths Class 11?

Yes, Extramarks updates its study material with all the new topics that get added to the syllabus. They leave no stone unturned to make sure that students do not have to face any difficulties. So, Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 are of the updated syllabus as experts always make changes whenever something new comes up.

### 4. Are Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 written topic-wise according to the NCERT book of Maths?

Yes, Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 has been written topic-wise according to the NCERT book of Maths. The experts always make sure that NCERT books stay the centre of their study material so that students will find it easier to find the questions in the book after reading from the Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5.