NCERT Solutions Class 11 Mathematics Chapter 1 – Sets
Students can start preparing for the upcoming exams with NCERT Solutions Class 11 Mathematics Chapter 1. It is made available for the students to get accustomed to the critical techniques to solve questions related to sets. Every student can get familiar with Chapter 1 Class 11 Mathematics concepts. With a considerable amount of time and practice, they will be able to perform better in the examination.
Sets are defined as the collection of objects. A set without any element is known as an empty set. Thus, the students will learn about definite elements and finite sets. They will understand how to calculate two sets and some properties of operation of the intersection. In addition, the students can also grasp their knowledge of the operations of unions and types of sets. All essential topics are covered in NCERT Solutions Class 11 Mathematics Chapter 1, such as powerset, subset, and singleton set.
Get access to NCERT Solutions and CBSE syllabus for both primary and secondary Classes from Extramarks website. Here are a few links for students to refer to primary Class solutions – NCERT solution Class 1, NCERT solution Class 2, NCERT solution Class 3, and NCERT solution Class 4.
Key Topics Covered In NCERT Solution for Class 11 Mathematics Chapter 1
It is essential to understand sets, not only for Maths but also for other subjects. Every student will understand the elements of sets and the operations that can be performed on them. Regular practice of Chapter 1 Mathematics Class 11 will help students acquire the knowledge necessary to perform functions on set elements. These solutions include examples and sample problems to help the students understand the topic step-by-step.
Thus, the following are the key topics covered in the NCERT Solutions Class 11 Mathematics Chapter 1:
| Exercises |
Topics |
| 1.1 |
Introduction to Sets |
| 1.2 |
Types of Sets |
| 1.3 |
Power Sets, Universal sets, and Subsets |
| 1.4 |
Union and Intersection |
| 1.5 |
Complementary Sets |
| 1.6 |
Operations around Sets |
| Other |
Miscellaneous |
1.1 Introduction to Sets
The introduction to sets and how they are represented begins with sets. The roaster form is a tabular presentation of a set. A set builder form is another way to represent a set. Students will be able to practice the questions in this exercise and learn more about these forms.
1.2 Types of Sets
This section focuses on understanding null sets, finite and infinite sets, and equal sets and their applications. For example, null sets are set without any elements. They can be a set of all odd numbers divisible by 2.
- Empty Sets: A set that does not contain any elements is empty, void set, or null. It is denoted with {} or Φ.
- Singleton Set: A single-element set is referred to as a singleton setup.
- Finite and Infinite Sets: A set that contains a limited number of elements is called a finite or infinite set.
- Equal Sets: If every element in A is also present in B, or vice versa, then A and B can be considered equal. Two equal sets will contain precisely the same element.
- Equivalent Sets are two finite sets A or B that are equivalent if they have the same number of elements, i.e. n(A) = n(B)
1.3 Power Sets, Universal Sets, and Subsets
This section in NCERT Solutions Class 11 Mathematics Chapter 1 is about power sets, subsets, and universal sets. It deals with problems based on correctly expressing statements using the correct symbols. Set theory symbols play a crucial role in the expression of ideas about subsets and related terms. This exercise provides multiple examples that illustrate the use of symbols in sets.
- Power Set: The collection of all subsets in a set is known as the power set. It is indicated by P(A). If A has more elements than A, i.e. If n(A), then the number of factors in A = n, then P(A) = 2n
- Universal Set: The universal set is a set that includes all sets within a given context.
- Subset: If all elements of set A belong to set B, set A can be considered a subset. We write symbols
A ⊆ B, if x ∈ A ⇒ x ∈ B
1.4 Union and Intersection
The sum of all elements in a set is called the union. The symbol for the union of sets, ‘U’, is used.
All elements common to given sets at the intersection are collected, called’∩’ (Uniformity of Sets).
The intersection of two sets A or B is denoted A B, common to both A AND B.
Thus, A ∩ B = {x : x ∈ A and x ∈ B}
1.5 Complementary Sets
It covers problems that arise from the complement of sets. A set’s complement is the sum of all elements in a set, excluding those found in its given sets. A’ is the complement to a set. This part of the exercise in NCERT Solutions Class 11 Mathematics Chapter 1 consists of seven problems based on the laws of double complementation, laws for the empty set, and universal set.
Let U be the universal collection, and A be a subset. Then, the complement is the set of elements U that are not A.
Thus, A’ = U – A = {x : x ∈ U and x ∉ A}
1.6 Operations around Sets
The union of two sets A, B and B, is denoted A B. It is the set that contains all elements found in either A or B or both. Thus, A ∪ B = {x : x ∈ A or x ∈ B}.
1.7 Miscellaneous
These problems are based on sets and their representations. They also include practical problems on the union and the intersection of sets. The sums are complex but can be used to help students learn this lesson. NCERT Solutions Class 11 Mathematics Chapter 1 miscellaneous section offers various types of problems. It is based on the operations of sets, application and subtraction of sets.
Different Laws of Algebra of Sets in NCERT Solutions Class 11 Mathematics Chapter 1
- Idempotent Laws: We have for any set A.
A ∪ A = A
A ∩ A = A
- Identity Laws: We have for any set A.
A ∪ Φ = A
A ∩ U = A
- CommutativeLaws: We have for any two sets A or B.
A ∪ B = B ∪ A
A ∩ B = B ∩ A
- Associative Laws: We have A, C, and B for any three sets.
A ∪ (B ∪ C) = (A ∪ B) ∪ C
A ∩ (B ∩ C) = (A ∩ B) ∩ C
- Distributive Laws: If A and B are three sets, then
A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
- De Morgan’s Laws If A or B are two sets, then
(A ∪ B)’ = A’ ∩ B’
(A ∩ B)’ = A’ ∪ B’
NCERT Solutions Class 11 Mathematics Chapter 1 Exercise & Solutions
NCERT Solutions Class 11 Mathematics Chapter 1 elaborates on the most fundamental concepts based on sets, types, and applications. The sets are majorly used to represent the relations and functions. The students can study the Class 11 Mathematics Chapter 1 with the help of NCERT solutions. It will help them make a foundation for upcoming topics such as geometry, sequences, and probability.
With the help of NCERT Solutions Class 11 Mathematics Chapter 1, the students can get well-versed with the topics and their applications in real-life situations. In the solutions guide for Class 11 Mathematics, we have covered a list of formulas, the union of sets, the intersection of sets, and the Venn diagram. Thus, the students will clearly understand all the terms and operations of settings. Further, it will also encourage them to enhance their speed while problem-solving .
The students can click on the below links to refer exercise specific questions and solutions for NCERT Solutions Class 11 Mathematics Chapter 1:
- Class 11 Maths Chapter 1 Ex 1.1 – 6 Questions
- Class 11 Maths Chapter 1 Ex 1.2 – 6 Questions
- Class 11 Maths Chapter 1 Ex 1.3 – 9 Questions
- Class 11 Maths Chapter 1 Ex 1.4 – 12 Questions
- Class 11 Maths Chapter 1 Ex 1.5 – 7 Questions
- Class 11 Maths Chapter 1 Ex 1.6 – 8 Questions
- Class 11 Maths Chapter 1 Miscellaneous Ex – 16 Questions
Apart from the exercise and solutions, the students can also refer to the NCERT solutions on our website.
- NCERT Solutions Class 6
- NCERT Solutions Class 7
- NCERT Solutions Class 8
- NCERT Solutions for Class 9
- NCERT Solutions for Class 10
- NCERT Solutions for Class 11
- NCERT Solutions for Class 12
NCERT Exemplar Class 11 Mathematics PDF
NCERT Exemplar acts as the best study material to test the knowledge on the topic and know your grey areas. r. It includes short-form questions, long-form questions, and multiple-choice questions. Further, the Exemplar contains various examples which have detailed solutions. Practising with the exemplar can help students strengthen their concepts on Sets-Chapter 1 Class 11.
Also, they can improve their knowledge and skills on the topic. The difficulty level varies from the topic given in a Chapter. For example, the difficulty level on Sets- Chapter 1 is moderate. So, it is suitable for Class 11, 12 and so on. Chapter 11 of NCERT Mathematics is on Sets. The Chapter defines Sets, Relations between Sets, a Product of Sets, Operations on Sets, and many more.
This Chapter deals with set theory in Mathematics which is a branch of algebra or Mathematical logic that deals with concepts related to the collection like union, intersection, complement, and so on. . This Chapter is necessary as it provides good practice to test how well you can apply your concepts on sets. The NCERT Exemplar gives a strong foundation in Mathematics..
To improve your score, the students can refer to NCERT Solutions Class 11 Mathematics Chapter 1 and other NCERT solutions. It is equally important to use the right reference materials from authentic, dependable, and reliable sources like Extramarks and be confident of the results.
Key Features of NCERT Solutions Class 11 Mathematics Chapter 1
Every student wishes to attain good marks in the examination. Thus, to get the best score, refer to NCERT Solutions Class 11 Mathematics Chapter 1. It offers a complete solution for all the complex examples. The key features in the solutions include:
- In Chapter 11 Sets, the students will be able to apply the concepts required to solve many sets of related problems.
- The NCERT solutions help clear doubts and obstacles by explaining the Chapter’s complex concepts.
- The solutions are provided with detailed explanations and presented by subject matter experts.
- With the help of NCERT Solutions Class 11 Mathematics Chapter 1, the students can gain knowledge of the concepts related to sets.
- Class 11 Mathematics NCERT solutions Chapter 1 helps the student get a strong foundation for the operations of sets.