CBSE Class 11 Mathematics Chapter 1: Sets NCERT Solutions

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NCERT Solutions PDF Class 11 PDF

This chapter introduces the fundamental concept of sets in mathematics, crucial for higher studies. The NCERT Solutions for Class 11 Mathematics, Chapter 1: Sets, provide detailed explanations and step-by-step solutions for all exercises. It covers the definition of a set, methods of representing sets (roster form and set-builder form), types of sets (empty set, finite and infinite sets, equal sets), subsets, intervals, and the universal set. The solutions are designed to help students grasp the properties of sets and apply them to solve various problems. This resource is ideal for exam preparation, offering clarity on definitions and problem-solving techniques to build a strong foundation in set theory.

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Quick info

BoardCBSE
ClassClass 11
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 1: Sets

Chapter summary

Chapter 1: Sets for CBSE Class 11 Mathematics lays the groundwork for understanding collections of objects. This NCERT Solutions guide focuses on defining sets, distinguishing between well-defined collections (sets) and those that are subjective (not sets). It covers representation methods like roster and set-builder forms, and introduces basic set types and concepts. The exercises are designed to test the student's ability to identify and describe sets accurately.

Learning outcomes

  • Understand the definition of a set as a well-defined collection.
  • Differentiate between sets and non-sets based on the criterion of well-definedness.
  • Identify elements belonging to a given set.
  • Justify whether a given collection constitutes a set.

Topics covered

Paper topics

  • Definition of a Set
  • Well-defined Collections
  • Identifying Sets
  • Elements of a Set
  • Months starting with J
  • Talented Writers
  • Best Cricket Batsmen
  • Boys in a Class
  • Natural Numbers less than 100
  • Novels by Munshi Prem Chand
  • Even Integers
  • Questions in a Chapter
  • Dangerous Animals

Important topics

  • Definition of a Set
  • Well-defined Collections
  • Distinguishing Sets from Non-sets
  • Justification of Set Membership

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Questions and Solutions

Question 1

Which of the following collections are sets? Justify your answer.
  1. The collection of all months of a year beginning with the letter J.
  2. The collection of ten most talented writers of India.
  3. A team of eleven best cricket batsmen of the world.
  4. The collection of all boys in your class.
  5. The collection of all natural numbers less than 100.
  6. A collection of novels written by the writer Munshi Prem Chand.
  7. The collection of all even integers.
  8. The collection of questions in this Chapter.
  9. A collection of most dangerous animals of the world.
Solution:

To determine if a collection is a set, we must check if it is 'well-defined'. A collection is well-defined if we can clearly and unambiguously determine whether a particular object belongs to the collection or not.

  1. The collection of all months of a year beginning with the letter J: This collection is a set. The months are January, June, and July. These are specific, identifiable months, making the collection well-defined.

  2. The collection of ten most talented writers of India: This collection is not a set. The term 'most talented' is subjective and varies from person to person. There is no objective criterion to determine who the ten most talented writers are, making the collection not well-defined.

  3. A team of eleven best cricket batsmen of the world: This collection is not a set. Similar to the previous point, 'best' is a subjective criterion. Different people will have different opinions on who the best batsmen are, so the collection is not well-defined.

  4. The collection of all boys in your class: This collection is a set. It is well-defined because you can objectively identify every boy who is a student in your class.

  5. The collection of all natural numbers less than 100: This collection is a set. It is well-defined because we can clearly identify all natural numbers (1, 2, 3, ...) that are less than 100.

  6. A collection of novels written by the writer Munshi Prem Chand: This collection is a set. It is well-defined because one can objectively list or identify all the novels authored by Munshi Prem Chand.

  7. The collection of all even integers: This collection is a set. It is well-defined because any integer can be checked to see if it is divisible by 2, thus determining its membership in the collection.

  8. The collection of questions in this Chapter: This collection is a set. It is well-defined because one can clearly identify and list all the questions present within this specific chapter.

  9. A collection of most dangerous animals of the world: This collection is not a set. The term 'most dangerous' is subjective and depends on various factors and perspectives. What one person considers dangerous, another might not, making the collection not well-defined.

Common mistakes

  • Confusing subjective collections with well-defined sets.
  • Not providing a clear justification for why a collection is or is not a set.
  • Ambiguity in interpreting 'talented', 'best', or 'dangerous' as criteria for set membership.

Revision tips

  • Focus on the definition of a 'set' and the 'well-defined' criterion.
  • Practice identifying elements for each given collection.
  • Ensure justifications for classifying collections as sets or not are clear and logical.

Practice MCQs

Q1. Which of the following is a well-defined collection and thus a set?

Q2. Why is 'The collection of ten most talented writers of India' not considered a set?

Q3. Which of these collections is a set?

Q4. The collection of all natural numbers less than 100 is considered a set because:

Q5. What makes 'The collection of all even integers' a set?

Frequently asked questions

What is the main concept covered in Chapter 1: Sets for Class 11 Maths?

Chapter 1 introduces the fundamental concept of sets as well-defined collections of objects and teaches how to identify them.

How do these NCERT Solutions help students?

These solutions provide clear, step-by-step explanations for each question in Exercise 1.1, helping students understand the criteria for a collection to be a set and how to justify their answers.

What is the key criterion for a collection to be called a set?

The key criterion is that the collection must be 'well-defined'. This means that for any given object, it must be possible to definitively say whether the object belongs to the collection or not.

Are subjective opinions important when determining if a collection is a set?

No, subjective opinions are precisely what make a collection *not* a set. For example, 'most talented writers' is subjective, whereas 'all boys in your class' is objective and well-defined.

Which types of collections are explicitly mentioned as *not* being sets in Exercise 1.1?

Collections based on subjective criteria like 'most talented writers', 'best cricket batsmen', and 'most dangerous animals' are identified as not being sets.

How can I use these solutions for revision?

Review the definition of a set and the 'well-defined' rule. Then, go through each question and its justification to reinforce your understanding of why certain collections are sets and others are not.

Important links

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