# NCERT Solutions for Class 11 Maths Chapter 1 Sets (Ex 1.3)

Students who have been promoted to Class 12 and chose to study Mathematics may find themselves challenged with topics that are new to their knowledge. They might have heard about some of the introductory chapters to new concepts and ideas like Limits and Derivatives, Sets, Functions, Complex Numbers, Permutations, Combinations, Mathematical Induction, Linear Inequalities, Binomial Theorem, Series and Three-Dimensional Geometry. All these chapters introduce a new topic that has not been mentioned in books before Class 11. But these chapters are important for studies in Class 11 and they also form the basis of the Class 12 books by NCERT. If students are struggling with any chapter, they can refer to Extramarks for assistance. Likely, they can refer to the NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3 for any additional help they need in this exercise of Chapter 1 of NCERT Class 11.

The NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3 can help students practice NCERT books. Students must remember that mathematics requires a lot of practice to get good marks. Students must perform exercises from NCERT. If they need any help with answering the questions, they can refer to the NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3. Learning new things can be challenging for students, and they might make mistakes in their solutions. They could find themselves struggling to identify their mistakes without external help. In those cases, the NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3, could be of help to students. Students may be able to find a better solution for the question, and they may also find the solution given in the NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3 less time-consuming. They can consider the NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3 for help with their studies while solving the Class 11 Maths Chapter 1 Sets Exercise 1.3. It will assist them with any doubts that may be clouding their minds.

Extramarks provides the NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3, so they can practice Exercise 1.3. Students should try to practice as much as they can in Mathematics. Practising is an integral part of the preparation for any exam. It requires a lot of practice for students to get correct answers on time during an exam. The NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3 can help students by providing time-efficient solutions to questions in NCERT Class 11 Maths Chapter 1 Exercise 1.3. There is no need for students to stress about this. Students should focus on studying and getting better if they find themselves struggling to solve answers correctly. They can always take support from their teachers and friends, and moreover, they can also find academic support with Extramarks’ NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3 for this particular chapter and other chapters too. The NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3 are a really good example of the quality study material provided by Extramarks.

## NCERT Solutions for Class 11 Maths Chapter 1 Sets (Ex 1.3) Exercise 1.3

The NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3 are for Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.3. It will help students understand how to answer the questions given in NCERT Class 12 Chapter 1 sets. It will help them interpret the questions correctly and then write the answer in a structured way. Students could make a few mistakes. It is natural for anyone to make mistakes in something when they are doing it for the first time. After a while, or when they just start to grasp the idea of a topic they have started studying recently, students can get a basic idea of solving problems. It is not important that they get the answer correct on the first try. But students must be willing to learn and correct their mistakes if they make any. They must be open to criticism and accept the help of teachers and their friends. They can also take academic help from Extramarks’ NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3 provided for this chapter on their app and website.

Students know that the NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3 are available to them for any help they require but they must know that they have to try to solve these questions by themselves. For that, they need to understand the topics related to this exercise first. They will have to know what it is about before starting to solve the exercise. Doing otherwise could lead them to forget the topics and ultimately, answer those questions wrong. The NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3 will help students to revise these topics and also to get an overview of what topics are included in this exercise. This will help them to be prepared for solving the questions. The NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3 are proven to be a helpful tool provided to students by Extramarks on their app and website.

Students must know their syllabus before they start their preparations for the Mathematics exam. It is important to go through the notes and NCERT solutions to perform well in exams. Students preparing for board exams must be aware of the accepted method of solution for any question. As in Mathematics, one question could probably be solved using many different methods and formulas that give the same answer. But the school or board might not find one or another method acceptable if they find it does not fit the criteria of their marking system. This could make students lose marks even after providing the correct answer. The NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3, can help students with their struggles with this.

### Access NCERT solutions for Math Chapter 1 – Sets Exercise 1.3

In the Chapter named – Sets, students get to learn about sets and their representation, the types of sets like Universal Sets, Empty Sets, Subset of a Set, the Venn Diagram, Union And Interaction of Sets, the Difference of Sets, Complement of a Set, Properties of Sets and practical problems related to Sets. It is applied to solve questions in various topics further in the book like probability, trigonometry, and also from the Class 12 books that they will be doing if they choose to continue studying Mathematics. The NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3 will help students understand sets, so they can apply them while solving questions in further exercises. Having already studied Sets would benefit them when solving related questions and concepts like Relations and Functions, which could turn into a struggle if not studied with concentration. Students must take any help they require regarding Exercise 1.3 of Class 11 from the NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3. Students must study and practice Sets to avoid having a problem in exams or when solving NCERT exercises. They could always take help in solving exercises through the use of NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3.

### Exercise 1.3

In the NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3, the importance of Exercise 1.3 can be seen by students through the answers provided by Extramarks.

Exercise 1.3 of NCERT Class 11 Chapter 1 – Sets is an important exercise in the preparation process for students. This exercise contains 9 questions in total. These questions are based on the topics of the types of sets like universal sets, power sets, finite and infinite sets, equal sets, empty sets, and subsets of a set. The new topics that were introduced after Exercise 1.2 and before Exercise 1.3 are subsets, intervals as subsets, power sets, and universal sets. This exercise is followed by the introduction of Venn diagrams, operations on sets like the union of sets, the intersection of sets, and differences of sets, and properties of operations on sets. Students should read the definitions of these new topics, so they are familiar with the topic they will be solving questions related. This exercise has nine questions that can be solved by studying the topics mentioned before in this paragraph. It should be noted that every topic is important as it helps answer questions further in the chapter. Students might have difficulties answering exercises after this one if they have not thoroughly solved all the questions without making mistake. The NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3, will help with the questions students have doubts about. Students can also check whether their answers are correct or not from NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3.

Therefore, students should solve all the exercises thoroughly before moving on to the next one. This will help them to avoid forgetting concepts related to it. This will improve their academic performance. The NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3 should be referred to by students when they begin their revision of Exercise 1.3. It will only benefit students if they are doing in-depth studies. Otherwise, they risk losing the knowledge of these concepts which could hinder their performance. Hence, students must consider taking help from the NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3.

### NCERT Solutions for Class 11 Maths Chapters

The NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3 are for students who want to improve their academic performance in terms of time taken to solve the question, the method of solution, the formula used for answering and the length of answers. This all could help them score better in their board exams. The NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3 is important for students who are going to be giving their board exams, especially CBSE Board exams, as NCERT books are a part of the curriculum for CBSE. It is used by teachers to teach students from basics to advance. NCERT can help students achieve their desired scores. Students must remember to solve all the exercises in the NCERT books of Class 11 for Mathematics. The NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3 will help students at any step they find themselves having difficulty. The NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3 will help students identify their mistakes and to correct their answers. The NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3 will also help them understand the concepts of the Exercise better.

These NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3, will help students perform well in any tests they take part in. The NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3 provided by Extramarks is a useful tool for preparation for exams. Students must remember the benefits of solving NCERT. They must go through the solutions of NCERT whether on the NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3 or the ones they prepared themselves as last-minute revision before exams. Going through the solutions to each exercise will give students a quick overview of the chapter.

### NCERT Solution Class 11 Maths of Chapter 1 All Exercises

It is important to solve all the exercises of a chapter. To gain confidence and knowledge for achieving good scores in exams, it is important to study all the chapters and exercises according to the syllabus. Studying only one exercise is not good and it should not be skipped because it may contain information that will be used later for other questions. All the exercises of NCERT Class 11 Mathematics Chapter 1- Sets must be done by the student to gain the required knowledge to solve all the questions from this chapter that comes in the exam.

Studying only the topics in one exercise will not be enough to score well. Hence, students must focus on studying all the exercises and practising them until they understand the topics of the whole chapter. The NCERT Book for Mathematics also has miscellaneous exercises that include questions from all over the chapter. In this exercise, questions of all types are present, and all the topics covered in the chapter are mentioned. This exercise has some very important questions that students must answer to gain confidence in their knowledge of the chapter and to understand how all the steps could be applied to specific questions. It will help students score well in their exams for entrance or board exams as well.

After this exercise, students will learn about the topics like Venn diagram, union and interaction of sets, the difference of sets, the complement of a set, properties of sets and practical problems related to sets. Solving the questions of these could turn out to be tricky for students if they have not studied Exercise 1.3 and the exercises before that carefully. Students can take help from the NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3 for that. It is important to understand all the exercises and their concepts one by one and also to solve them without mistakes. Students must know that they can take help from other students and teachers if they feel unsure about one question. The exercises followed always provide knowledge about a new topic that has not been introduced till now. So students must focus to get the scores they need for their exams.

### NCERT Solutions For Class 11 Math Chapter 1 Sets Exercise 1.3 PDF Download

The NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3, are available on Extramarks’ website and app for students to study from. Practising this exercise will help them form a deeper understanding of Chapter 1 of Class 11. Students must practise this exercise to understand the concepts of subsets and the types of sets like universal sets, power sets, equal sets, empty sets, finite sets, and infinite sets. These topics should be practised by students through the NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3 as much as they can. Practising is of most importance in Mathematics. Not only the NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3, but students must practice all the exercises of Chapter 1 Sets of NCERT of Class 11.

### Topics Covered in Exercise 1.3 of Class 11 NCERT Math

Exercise 1.3 of Class 11 is about subsets and the types of sets like universal sets, power sets, equal sets, empty sets, finite sets and infinite sets, students can also get this overview of the exercise on the NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3. The types of sets have been defined with examples, so students can easily understand and predict which type of set a given set or subset is. This will help students solve Exercise 1.3 of NCERT Chapter 1 Sets. Not only Exercise 1.3 but also other exercises are followed by it. It will help students boost their confidence in these topics and improve their performance in the exam. Improved performance will help them with their academics and also help them perform better in other exams they choose to participate in. it will give them the confidence to participate more and go for further education. Good marks are required by students to get a college of their choice and their desired program.

The NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3 provide correct answers with explanations for students to understand the concepts given in Exercise 1.3. Students must remember that every exercise of NCERT is important, including Exercise 1.3 and solutions of this exercise are given in the NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3. The topics covered in Exercise 1.3 are important for students to understand as they will help them determine how different types of questions should be solved, and it will help students if they know the properties of different types of sets. This will help them when solving problems where minimal information is provided by the question. In those cases, it could help students to know what the question has mentioned and if they are able to correctly interpret the question and the type of set, they will be able to solve the question if they remember the properties of that subset. Hence, students must study and remember this topic. They should get help from the NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3 if need be. Any doubt from Exercise 1.3 can be solved by going through the NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3. Topics covered in exercise 1.3 are important for students’ examinations.

### NCERT Solutions for Class 11 Maths Chapter 1 Sets (Ex 1.3) Exercise 1.3

The NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3 provided by Extramarks is very important for the entrance that students choose to give after they have passed out from Class 12. This will give them the opportunity to solve the questions themselves and correct their mistakes. Having this knowledge will help them solve the problems given in sample papers, mock tests, or any other tests they take. It will help them to enhance their performance when they appear for the exam. The NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3 will help the students understand the concept of subsets and the types of sets like universal sets, power sets, equal sets, empty sets, finite sets and infinite sets on which exercise 1.3 is based. The NCERT Solutions For Class 11 Maths Chapter 1 Exercise 1.3, provide students with a way to improve their method of providing solutions when solving Exercise 1.3 and to make the representation of their work better to get better marks in their exam.

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**Q.1 ** Make correct statements by filling in symbols ⊂ or in the blank spaces:

$\begin{array}{l}\left(\text{i}\right)\text{\hspace{0.33em}}\left\{2,3,4\right\}...\left\{1,2,3,4,5\right\}\\ \left(\mathrm{ii}\right)\text{\hspace{0.33em}}\left\{\text{a},\text{b},\text{c}\right\}...\left\{\text{b},\text{c},\text{d}\right\}\\ \left(\mathrm{iii}\right)\text{\hspace{0.33em}}\left\{\begin{array}{l}\text{x}:\mathrm{x}\text{\hspace{0.33em}}\mathrm{is}\text{\hspace{0.33em}}\mathrm{a}\text{\hspace{0.33em}}\mathrm{student}\text{\hspace{0.33em}}\mathrm{of}\\ \mathrm{Class}\text{\hspace{0.33em}}\mathrm{XI}\text{\hspace{0.33em}}\mathrm{of}\text{\hspace{0.33em}}\mathrm{your}\text{\hspace{0.33em}}\mathrm{school}\end{array}\right\}...\left\{\begin{array}{l}\text{x}:\mathrm{x}\text{\hspace{0.33em}}\mathrm{student}\text{\hspace{0.33em}}\mathrm{of}\text{\hspace{0.33em}}\mathrm{your}\\ \mathrm{school}\end{array}\right\}\\ \left(\mathrm{iv}\right)\text{\hspace{0.33em}}\left\{\begin{array}{l}\text{x}:\mathrm{x}\text{\hspace{0.33em}}\mathrm{is}\text{\hspace{0.33em}}\mathrm{a}\text{\hspace{0.33em}}\mathrm{circle}\\ \mathrm{in}\text{\hspace{0.33em}}\mathrm{the}\text{\hspace{0.33em}}\mathrm{plane}\end{array}\right\}...\left\{\begin{array}{l}\text{x}:\mathrm{x}\text{\hspace{0.33em}}\mathrm{is}\text{\hspace{0.33em}}\mathrm{a}\text{\hspace{0.33em}}\mathrm{circle}\text{\hspace{0.33em}}\mathrm{in}\text{\hspace{0.33em}}\mathrm{the}\text{\hspace{0.33em}}\mathrm{same}\\ \mathrm{plane}\text{\hspace{0.33em}}\mathrm{with}\text{\hspace{0.33em}}\mathrm{radius}\text{\hspace{0.33em}}1\text{\hspace{0.33em}}\mathrm{unit}\end{array}\right\}\\ \left(\text{v}\right)\text{\hspace{0.33em}}\left\{\begin{array}{l}\text{x}:\mathrm{x}\text{\hspace{0.33em}}\mathrm{is}\text{\hspace{0.33em}}\mathrm{a}\text{\hspace{0.33em}}\mathrm{triangle}\\ \mathrm{in}\text{\hspace{0.33em}}\mathrm{a}\text{\hspace{0.33em}}\mathrm{plane}\end{array}\right\}...\left\{\begin{array}{l}\text{x}:\mathrm{x}\text{\hspace{0.33em}}\mathrm{is}\text{\hspace{0.33em}}\mathrm{a}\text{\hspace{0.33em}}\mathrm{rectangle}\\ \mathrm{in}\text{\hspace{0.33em}}\mathrm{the}\text{\hspace{0.33em}}\mathrm{plane}\end{array}\right\}\\ \left(\mathrm{vi}\right)\text{\hspace{0.33em}}\left\{\begin{array}{l}\text{x}:\mathrm{x}\text{\hspace{0.33em}}\mathrm{is}\text{\hspace{0.33em}}\mathrm{an}\text{\hspace{0.33em}}\mathrm{equilateral}\\ \mathrm{triangle}\text{\hspace{0.33em}}\mathrm{in}\text{\hspace{0.33em}}\mathrm{a}\text{\hspace{0.33em}}\mathrm{plane}\end{array}\right\}...\left\{\begin{array}{l}\text{x}:\mathrm{x}\text{\hspace{0.33em}}\mathrm{is}\text{\hspace{0.33em}}\mathrm{a}\text{\hspace{0.33em}}\mathrm{triangle}\text{\hspace{0.33em}}\mathrm{in}\\ \mathrm{the}\text{\hspace{0.33em}}\mathrm{same}\text{\hspace{0.33em}}\mathrm{plane}\end{array}\right\}\\ \left(\mathrm{vii}\right)\text{\hspace{0.33em}}\left\{\begin{array}{l}\text{x}:\mathrm{x}\text{\hspace{0.33em}}\mathrm{is}\text{\hspace{0.33em}}\mathrm{an}\text{\hspace{0.33em}}\mathrm{even}\\ \mathrm{natural}\text{\hspace{0.33em}}\mathrm{number}\end{array}\right\}...\left\{\text{x}:\mathrm{x}\text{\hspace{0.33em}}\mathrm{is}\text{\hspace{0.33em}}\mathrm{an}\text{\hspace{0.33em}}\mathrm{integer}\right\}\end{array}$

**Ans.**

$\begin{array}{l}\left(\text{i}\right)\text{\hspace{0.33em}}\left\{2,3,4\right\}\subset \left\{1,2,3,4,5\right\}\\ \left(\mathrm{ii}\right)\text{\hspace{0.33em}}\left\{\text{a},\text{b},\text{c}\right\}\not\subset \left\{\text{b},\text{c},\text{d}\right\}\\ \left(\mathrm{iii}\right)\text{\hspace{0.33em}}\left\{\begin{array}{l}\text{x}:\mathrm{x}\text{\hspace{0.33em}}\mathrm{is}\text{\hspace{0.33em}}\mathrm{a}\text{\hspace{0.33em}}\mathrm{student}\text{\hspace{0.33em}}\mathrm{of}\text{\hspace{0.33em}}\mathrm{Class}\\ \mathrm{XI}\text{\hspace{0.33em}}\mathrm{of}\text{\hspace{0.33em}}\mathrm{your}\text{\hspace{0.33em}}\mathrm{school}\end{array}\right\}\subset \left\{\begin{array}{l}\text{x}:\mathrm{x}\text{\hspace{0.33em}}\mathrm{student}\text{\hspace{0.33em}}\mathrm{of}\text{\hspace{0.33em}}\mathrm{your}\\ \mathrm{school}\end{array}\right\}\\ \left(\mathrm{iv}\right)\text{\hspace{0.33em}}\left\{\begin{array}{l}\text{x}:\mathrm{x}\text{\hspace{0.33em}}\mathrm{is}\text{\hspace{0.33em}}\mathrm{a}\text{\hspace{0.33em}}\mathrm{circle}\\ \mathrm{in}\text{\hspace{0.33em}}\mathrm{the}\text{\hspace{0.33em}}\mathrm{plane}\end{array}\right\}\not\subset \left\{\begin{array}{l}\text{x}:\mathrm{x}\text{\hspace{0.33em}}\mathrm{is}\text{\hspace{0.33em}}\mathrm{a}\text{\hspace{0.33em}}\mathrm{circle}\text{\hspace{0.33em}}\mathrm{in}\text{\hspace{0.33em}}\mathrm{the}\text{\hspace{0.33em}}\mathrm{same}\\ \mathrm{plane}\text{\hspace{0.33em}}\mathrm{with}\text{\hspace{0.33em}}\mathrm{radius}\text{\hspace{0.33em}}1\text{\hspace{0.33em}}\mathrm{unit}\end{array}\right\}\\ \left(\text{v}\right)\text{\hspace{0.33em}}\left\{\begin{array}{l}\text{x}:\mathrm{x}\text{\hspace{0.33em}}\mathrm{is}\text{\hspace{0.33em}}\mathrm{a}\text{\hspace{0.33em}}\mathrm{triangle}\\ \mathrm{in}\text{\hspace{0.33em}}\mathrm{a}\text{\hspace{0.33em}}\mathrm{plane}\end{array}\right\}\not\subset \left\{\begin{array}{l}\text{x}:\mathrm{x}\text{\hspace{0.33em}}\mathrm{is}\text{\hspace{0.33em}}\mathrm{a}\text{\hspace{0.33em}}\mathrm{rectangle}\\ \mathrm{in}\text{\hspace{0.33em}}\mathrm{the}\text{\hspace{0.33em}}\mathrm{plane}\end{array}\right\}\\ \left(\mathrm{vi}\right)\text{\hspace{0.33em}}\left\{\begin{array}{l}\text{x}:\mathrm{x}\text{\hspace{0.33em}}\mathrm{is}\text{\hspace{0.33em}}\mathrm{an}\text{\hspace{0.33em}}\mathrm{equilateral}\\ \mathrm{triangle}\text{\hspace{0.33em}}\mathrm{in}\text{\hspace{0.33em}}\mathrm{a}\text{\hspace{0.33em}}\mathrm{plane}\end{array}\right\}\subset \left\{\begin{array}{l}\text{x}:\mathrm{x}\text{\hspace{0.33em}}\mathrm{is}\text{\hspace{0.33em}}\mathrm{a}\text{\hspace{0.33em}}\mathrm{triangle}\text{\hspace{0.33em}}\mathrm{in}\\ \mathrm{the}\text{\hspace{0.33em}}\mathrm{same}\text{\hspace{0.33em}}\mathrm{plane}\end{array}\right\}\\ \left(\mathrm{vii}\right)\text{\hspace{0.33em}}\left\{\begin{array}{l}\text{x}:\mathrm{x}\text{\hspace{0.33em}}\mathrm{is}\text{\hspace{0.33em}}\mathrm{an}\text{\hspace{0.33em}}\mathrm{even}\\ \mathrm{natural}\text{\hspace{0.33em}}\mathrm{number}\end{array}\right\}\subset \left\{\text{x}:\mathrm{x}\text{\hspace{0.33em}}\mathrm{is}\text{\hspace{0.33em}}\mathrm{an}\text{\hspace{0.33em}integer}\right\}\end{array}$

**Q.2 **

$\begin{array}{l}\text{Examine whether the following statements are true or false:}\\ \left(\text{i}\right)\text{{a,b}}\not\subset \text{{b,c, a}}\\ \left(\text{ii}\right)\text{{a,e}}\subset \text{{x : x is a vowel in the English alphabet}}\\ \left(\text{iii}\right)\text{}\left\{\text{1, 2, 3}\right\}\subset \text{{ 1, 3,5}}\\ \left(\text{iv}\right)\text{{a}}\subset \text{{a,b, c}}\\ \left(\text{v}\right)\text{{a}}\in \text{{a,b, c}}\\ \left(\text{vi}\right)\text{}\left\{\begin{array}{l}\text{x : x is an even natural}\\ \text{number less than 6}\end{array}\right\}\subset \left\{\begin{array}{l}\text{x : x is a natural number}\\ \text{which divides 36}\end{array}\right\}\end{array}$

**Ans.**

$\begin{array}{l}\left(\text{i}\right)\text{{a,b}}\not\subset \text{{b,c, a}}\to \text{False}\\ \left(\text{ii}\right)\text{{a,e}}\subset \text{{x : x is a vowel in the English alphabet}}\to \text{True}\\ \left(\text{iii}\right)\text{}\left\{\text{1, 2, 3}\right\}\subset \text{{ 1, 3,5}}\to \text{False}\\ \left(\text{iv}\right)\text{{a}}\subset \text{{a,b, c}}\to \text{True}\\ \left(\text{v}\right)\text{{a}}\in \text{{a,b, c}}\to \text{False}\\ \left(\text{vi}\right)\text{}\left\{\begin{array}{l}\text{x : x is an even natural}\\ \text{number less than 6}\end{array}\right\}\subset \left\{\begin{array}{l}\text{x : x is a natural number}\\ \text{which divides 36}\end{array}\right\}\text{}\to \text{True}\end{array}$

**Q.3 ** Let A = {1, 2, {3, 4}, 5}. Which of the following statements are incorrect and why?

(i) {3, 4} ⊂ A

(ii) {3, 4} ∈ A

(iii) {{3, 4}} ⊂ A

(iv) 1 ∈ A

(v) 1 ⊂ A

(vi) {1, 2, 5} ⊂ A

(vii) {1, 2, 5} ∈ A

(viii) {1, 2, 3} ⊂ A

(ix) Φ ∈ A

(x) Φ ⊂ A

(xi) {Φ} ⊂ A

**Ans.**

(i) {3, 4}⊂ A —-Incorrect statement.

Correct statement is {3, 4} ∈ A

(ii) {3, 4} ∈ A —- Correct statement.

(iii) {{3, 4}} ⊂ A—- Correct statement.

(iv) 1 ∈ A —- Correct statement.

(v) 1 ⊂ A —-Incorrect statement.

Correct statement is 1 ∈ A

(vi) {1, 2, 5} ⊂ A —- Correct statement.

(vii) {1, 2, 5} ∈ A —- Incorrect statement.

Correct statement is {1, 2, 5} ⊂ A

(viii) {1, 2, 3} ⊂ A —- Incorrect statement.

Because 3 is not individual element of set A.

(ix) φ ∈ A—- Incorrect statement.

Since, φ is a subset of set A.

(x) φ ⊂ A —- Correct statement.

(xi) {φ} ⊂ A —- Incorrect statement.

Since, φ is not an element of set A.

**Q.4 ** Write down all the subsets of the following sets

(i) {a}

(ii) {a, b}

(iii) {1, 2, 3}

(iv) Φ

**Ans.**

(i) Subsets of {a} are: {}, {a}.

(ii) Subsets of {a, b} are: {}, {a}, {b}, {a, b}.

(iii) Subsets of {1, 2, 3} are: {}, {1}, {2}, {3},{1, 2}, {1, 3}, {2, 3}, {1, 2, 3}.

(iv) Subset of Φ is Φ only.

**Q.5 ** How many elements has P(A), if A = Φ?

**Ans.**

P(A) is called power set of set A. It is the collection of subsets of set A. Since, there is no element in set A, so there will be one subset of Φ.

Thus, P(A) = 1.

**Q.6 ** Write the following as intervals:

(i) {x: x ∈ R, – 4 < x ≤ 6}

(ii) {x: x ∈ R, – 12 < x < –10}

(iii) {x: x ∈ R, 0 ≤ x < 7}

(iv) {x: x ∈ R, 3 ≤ x ≤ 4}

**Ans.**

S. No. | Set builder form of interval | Intervals |

(i) | {x: x ∈ R, – 4 < x ≤ 6} | (– 4, 6] |

(ii) | {x: x ∈ R, – 12 < x < –10} | (– 12, – 10) |

(iii) | {x: x ∈ R, 0 ≤ x < 7} | [0, 7) |

(iv) | {x: x ∈ R, 3 ≤ x ≤ 4} | [3, 4] |

**Q.7 ** Write the following intervals in set-builder form:

(i) (– 3, 0)

(ii) [6, 12]

(iii) (6, 12]

(iv) [–23, 5)

**Ans.**

S. No. | interval | Set builder form of intervals |

(i) | (– 3 , 0) | {x: x ∈ R, – 3 < x < 0} |

(ii) | [6, 12] | {x: x ∈ R, 6 ≤ x ≤ 12} |

(iii) | (6, 12] | {x: x ∈ R, 6 < x ≤ 12} |

(iv) | [–23, 5) | {x: x ∈ R, – 23 ≤ x < 5} |

**Q.8 ** What universal set(s) would you propose for each of the following:

(i) The set of right triangles.

(ii) The set of isosceles triangles.

**Ans.**

(i) Universal set for the set of right triangles is set of triangles or set of polygons.

(ii) Universal set for the set of isosceles triangles is the set of triangles or set of polygons.

**Q.9 ** Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universal set (s) for all the three sets A, B and C

(i) {0, 1, 2, 3, 4, 5, 6}

(ii) Φ

(iii) {0,1,2,3,4,5,6,7,8,9,10}

(iv) {1, 2, 3, 4, 5, 6, 7, 8}

**Ans.**

(i) Since, elements of sets A and B are in {0, 1, 2, 3, 4, 5, 6} but elements of set C are not contained in {0, 1, 2, 3, 4, 5, 6}. So, {0, 1, 2, 3, 4, 5, 6} is not a universal set (s).

(ii) Since, elements of sets A, B and C are not contained in Φ. So, it is not a universal set.

(iii) Since, all the elements of sets A, B and C are in given set. So, {0,1,2,3,4,5,6,7,8,9,10} is a universal set (s) for all the three sets A, B and C.

(iv) Since, elements of set C are not in given set {1, 2, 3, 4, 5, 6, 7, 8}, so it is not a universal set(s) of all the three sets A, B and C.

## FAQs (Frequently Asked Questions)

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