NCERT Solutions Class 11 Maths Chapter 1 helps you understand Sets through detailed solutions covering roster and set-builder forms, types of sets (empty, finite, infinite), Venn diagrams, and set operations like union, intersection, and complement. You’ll learn how to solve problems on subsets, power sets, and De Morgan’s laws with practical examples that build your foundation for relations, functions, and probability in higher mathematics. Each solution includes step-by-step methods to tackle exam questions confidently.
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All exercises with step-by-step solutions | Updated 2025-26 | Free Download
Download PDF (Free)NCERT Solutions Class 11 Maths Chapter 1 Sets – Complete Guide
NCERT Class 11 Chapter 1 on Sets introduces you to one of the most fundamental concepts in modern mathematics. You’ll explore how sets provide a language to describe collections of objects and form the basis for various branches of mathematics including algebra, geometry, and calculus. This chapter carries significant weightage of 8 marks in CBSE board exams, making it crucial for your overall performance.
📊 CBSE Class 11 Maths Chapter 1 – Exam Weightage & Marking Scheme
| CBSE Board Marks | 8 Marks |
| Unit Name | Sets and Functions |
| Difficulty Level | Medium |
| Importance | High |
| Exam Types | CBSE Board, State Boards |
| Typical Questions | 2-3 questions |
You will learn about different types of sets such as empty sets, finite and infinite sets, equal sets, and subsets. The chapter thoroughly covers set operations including union, intersection, difference, and complement, along with their properties and laws. You’ll master Venn diagrams, which provide visual representations of sets and make complex problems easier to solve. These diagrams are particularly helpful in solving word problems that frequently appear in CBSE exams.
This chapter includes various question types in board exams: MCQs testing basic definitions (1-2 marks), short answer questions on set operations (2-3 marks), and long answer questions involving practical applications (4-5 marks). You’ll encounter real-world applications like organizing data, understanding probability concepts, and solving logical reasoning problems. The De Morgan’s laws and properties of set operations are especially important for competitive exams beyond CBSE.
Quick Facts – Class 11 Chapter 1
| 📖 Chapter Number | Chapter 1 |
| 📚 Chapter Name | Sets |
| ✏️ Total Exercises | 5 Exercises |
| ❓ Total Questions | 39 Questions |
| 📅 Updated For | CBSE Session 2025-26 |
Mastering sets is essential as it connects directly to Relations and Functions (Chapter 2) and forms the foundation for topics in Class 12 like Probability and Mathematical Reasoning. With consistent practice of NCERT solutions and previous year CBSE questions, you’ll build strong problem-solving skills that will benefit you throughout your mathematical journey.
NCERT Solutions Class 11 Maths Chapter 1 – All Exercises PDF Download
Download exercise-wise NCERT Solutions PDFs for offline study
| Exercise No. | Topics Covered | Download PDF |
|---|---|---|
| EXERCISE 1.1 | Complete step-by-step solutions for 6 questions | 📥 Download PDF |
| EXERCISE 1.2 | Complete step-by-step solutions for 6 questions | 📥 Download PDF |
| EXERCISE 1.3 | Complete step-by-step solutions for 8 questions | 📥 Download PDF |
| EXERCISE 1.4 | Complete step-by-step solutions for 12 questions | 📥 Download PDF |
| EXERCISE 1.5 | Complete step-by-step solutions for 7 questions | 📥 Download PDF |
Sets – Key Formulas & Concepts
Quick reference for CBSE exams
| Formula | Description | When to Use |
|---|---|---|
| Cardinality of Union of Two Sets \(n(A \cup B) = n(A) + n(B) – n(A \cap B)\) | Finds the number of elements in the union of two sets A and B. Note: Remember to subtract the intersection to avoid counting those elements twice. If A and B are disjoint (no common elements), then n(A ∩ B) = 0. | When you are given the number of elements in sets A, B, and their intersection, and need to find the number of elements in their union. |
| Cardinality of Union of Three Sets \(n(A \cup B \cup C) = n(A) + n(B) + n(C) – n(A \cap B) – n(B \cap C) – n(A \cap C) + n(A \cap B \cap C)\) | Finds the number of elements in the union of three sets A, B, and C. Note: This is an extension of the two-set formula. Pay close attention to the signs! | When you are given the number of elements in sets A, B, C, their pairwise intersections, and their triple intersection, and need to find the number of elements in their union. |
| De Morgan’s Law (Union) \((A \cup B)’ = A’ \cap B’\) | The complement of the union of two sets is equal to the intersection of their complements. Note: Remember that ‘ means complement. This law helps distribute the complement operation. | When simplifying complex set expressions involving complements and unions, or proving set identities. |
| De Morgan’s Law (Intersection) \((A \cap B)’ = A’ \cup B’\) | The complement of the intersection of two sets is equal to the union of their complements. Note: Similar to the other De Morgan’s Law, but with union and intersection swapped. | When simplifying complex set expressions involving complements and intersections, or proving set identities. |
| Subset Condition \(A \subseteq B \iff A \cap B = A\) | A is a subset of B if and only if the intersection of A and B is equal to A. Note: If every element of A is also in B, then taking the intersection will simply give you A back. | To prove that one set is a subset of another using intersection. |
| Power Set Cardinality \(n(P(A)) = 2^{n(A)}\) | The number of subsets (elements) in the power set of A is 2 raised to the power of the number of elements in A. Note: P(A) is the power set of A. Remember that the empty set is always a subset. | To find the total number of subsets (including the empty set and the set itself) of a given set. |
| Difference of Sets \(A – B = A \cap B’\) | The difference between set A and set B is the set of all elements that are in A but not in B. Note: A – B is read as ‘A minus B’ or ‘A difference B’. It is equivalent to the intersection of A with the complement of B. | When asked to find all elements that belong to A but not to B. |
| Symmetric Difference of Sets \(A \Delta B = (A – B) \cup (B – A)\) | The symmetric difference of sets A and B is the set of elements which are in either A or B, but not in both. Note: It’s also equivalent to (A ∪ B) – (A ∩ B). It represents the ‘exclusive or’ operation. | When asked to find the elements that are unique to either A or B, but not common to both. |
| Complement of a Set \(A’ = U – A\) | The complement of a set A is the set of all elements in the universal set U that are not in A. Note: The universal set U must be defined. The complement depends on what the universal set is. | When you need to find all elements that are NOT in a specific set. |
Frequently Asked Questions – NCERT Class 11 Maths Chapter 1
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