NCERT Solutions for Class 11 Maths Chapter 1 – Sets
Chapter 1 of Class 11 Mathematics introduces you to one of the most foundational concepts in mathematics — Sets. If you have ever grouped things based on a common property, you already have an intuitive sense of what a set is. This chapter, as prescribed by NCERT for the CBSE curriculum, formally defines sets, explores different types, and builds the algebraic language used throughout higher mathematics. Whether you are preparing for your board exams, JEE, or simply trying to clear the concept from scratch, these NCERT Solutions offer step-by-step, examiner-friendly answers to every question in the textbook.
Each solution is written with clarity so you understand not just the answer, but the reasoning behind it — helping you apply the same logic to new problems confidently. From understanding the roster form and set-builder form in Exercise 1.1, to mastering Venn diagrams and De Morgan's Laws in the later exercises, every solution here follows the NCERT method. No shortcuts, no skipped steps. The solutions are structured to match exactly how CBSE expects answers to be written. For all Chapters must, read NCERT Solutions for Class 11 Maths and subject-wise NCERT Solutions for Class 11.
Download PDFs – All Exercises of NCERT Solutions for Class 11 Maths Chapter 1 Sets
Click any exercise card below to download the free PDF of its solved solutions. All PDFs are based on the latest NCERT textbook edition.
Understanding Chapter 1 – Sets: Concepts, Theory & Key Formulas
At its heart, a Set is a well-defined collection of objects. The word "well-defined" is crucial — it means there is no ambiguity about whether a particular element belongs to the collection or not. For example, "a collection of natural numbers less than 10" is well-defined (1, 2, 3... 9), but "a collection of beautiful paintings" is not, because beauty is subjective.
Sets are usually denoted by capital letters — A, B, C — and their elements are listed inside curly braces. The study of sets gives you the mathematical vocabulary to talk about groups, relationships, and logical operations that appear throughout algebra, probability, and calculus. What makes this chapter rewarding is how it connects everyday grouping logic to precise mathematical notation.
Types of Sets — Quick Reference
Knowing the name and definition of each type of set is non-negotiable for this chapter. Here is every type you will encounter in the NCERT exercises:
| Type of Set | Definition | Example | Level |
|---|---|---|---|
| Empty Set (Null Set) | A set with no elements at all. Denoted by {} or ∅. | Set of months with 32 days = ∅ | Basic |
| Singleton Set | A set that has exactly one element. | {5} or {Monday} | Basic |
| Finite Set | A set whose elements can be counted and the count ends. | A = {2, 4, 6, 8, 10} | Basic |
| Infinite Set | A set whose elements cannot be exhausted by counting. | Set of all natural numbers: ℕ | Basic |
| Equal Sets | Two sets A and B are equal if every element of A is in B and vice versa. | {1,2,3} = {3,1,2} | Medium |
| Equivalent Sets | Sets with the same number of elements (same cardinality), not necessarily same elements. | {a,b,c} and {1,2,3} are equivalent | Medium |
| Subset | A is a subset of B (A ⊆ B) if every element of A belongs to B. | {1,2} ⊆ {1,2,3,4} | Medium |
| Proper Subset | A ⊂ B when A ⊆ B but A ≠ B (at least one extra element in B). | {1,2} ⊂ {1,2,3} | Medium |
| Power Set | The set of all subsets of A. If |A| = n, then |P(A)| = 2ⁿ. | A = {a,b} → P(A) = {∅,{a},{b},{a,b}} | Hard |
| Universal Set | The largest set that contains all sets under discussion (denoted by U). | U = set of all integers (when discussing even/odd) | Basic |
Set Operations — Formulas & Notation
These operations are the backbone of Exercises 1.4 and 1.5, and appear repeatedly in real-life problems (Exercise 1.6).
| Operation | Symbol | Meaning | Venn Diagram Region |
|---|---|---|---|
| Union | A ∪ B | All elements in A or B or both | Entire shaded area of both circles |
| Intersection | A ∩ B | Elements present in both A and B | Overlapping region only |
| Difference | A − B | Elements in A but NOT in B | Left circle only, excluding overlap |
| Complement | A′ or Aᶜ | All elements in U but NOT in A | Everything outside A's circle |
| Symmetric Difference | A Δ B | (A − B) ∪ (B − A); elements in either but not both | Both circles excluding the overlap |
Important Formulas You Cannot Ignore
n(A ∪ B) = n(A) + n(B) − n(A ∩ B) n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A ∩ B) − n(B ∩ C) − n(A ∩ C) + n(A ∩ B ∩ C) De Morgan's Laws: (A ∪ B)′ = A′ ∩ B′ (A ∩ B)′ = A′ ∪ B′ Power Set: If |A| = n, then |P(A)| = 2ⁿ
Exercise-wise Focus Areas at a Glance
Exercise 1.1
Identifying sets from descriptions, writing in roster form and set-builder form. Tests the very definition of a well-defined set.
Exercise 1.2
Distinguishing empty sets, finite sets, and infinite sets. Includes tricky questions where a set may look finite but is actually infinite.
Exercise 1.3
Subsets and power sets. Counting the number of subsets using 2ⁿ formula is tested here with multiple variations.
Exercise 1.4
Union and intersection using Venn diagrams. Both symbolic and diagram-based questions appear. Must practise drawing clear Venn diagrams.
Exercise 1.5
Complement of a set and De Morgan's Laws. Proof-based questions are common — understanding logic matters here, not just formulas.
Exercise 1.6
Real-life word problems using cardinality formulas. These are the most exam-relevant — surveys, groups, and overlapping categories.
Methods of Representing a Set
NCERT uses two primary methods to represent sets, and you are expected to convert between them in Exercise 1.1.
| Method | Also Called | How It Works | Example |
|---|---|---|---|
| Roster Form | Tabular Form / List Form | All elements listed inside { }, separated by commas. Order doesn't matter; no repetition. | A = {1, 2, 3, 4, 5} |
| Set-Builder Form | Rule Form / Property Form | Elements described by a common property using the notation {x : condition on x}. | A = {x : x ∈ ℕ, x ≤ 5} |
Study Tips for Chapter 1 from Toppers
- Always verify whether a set is well-defined before writing it — this alone can earn or lose 1 mark.
- For power sets, draw a tree diagram if the set has more than 2 elements to avoid missing any subset.
- Practise converting between roster and set-builder form both ways — NCERT exercises test both directions.
- In Exercise 1.6, always define what U, A, and B represent in your answer before applying the formula. Examiners reward clear variable definition.
- De Morgan's Laws have proof-based questions in the miscellaneous exercise — practise writing the proof step by step, not just stating the law.
Chapter Summary — Everything in One View
| Topic | Key Idea | Appears In | Exam Weightage |
|---|---|---|---|
| Definition of a Set | Well-defined collection of distinct objects | Ex 1.1 | 1–2 marks |
| Roster & Set-Builder Form | Two ways to represent any set | Ex 1.1 | 2–3 marks |
| Types of Sets | Empty, finite, infinite, equal, equivalent | Ex 1.2 | 2 marks |
| Subsets & Power Sets | A ⊆ B; |P(A)| = 2ⁿ | Ex 1.3 | 3–4 marks |
| Union & Intersection | A ∪ B, A ∩ B via Venn diagrams | Ex 1.4 | 4–5 marks |
| Complement & De Morgan's Laws | (A ∪ B)′ = A′ ∩ B′ and (A ∩ B)′ = A′ ∪ B′ | Ex 1.5, Misc. | 4–5 marks |
| Cardinality Formula | n(A ∪ B) = n(A) + n(B) − n(A ∩ B) | Ex 1.6, Misc. | 5–6 marks |
FAQs for NCERT Solutions for Class 11 Maths Chapter 1 Sets
Sets are one of the most fundamental concepts in mathematics. A set is a well-defined collection of objects, numbers, or elements. In Class 11 Maths, students learn different types of sets, including finite sets, infinite sets, equal sets, and subsets. Understanding sets is important because they form the basis of many advanced mathematical topics such as relations, functions, probability, and statistics. NCERT Solutions help students understand set notation, operations on sets, and Venn diagrams through step-by-step explanations. A strong understanding of sets helps improve logical thinking and problem-solving skills, making this chapter an essential foundation for higher mathematics and competitive examinations.
NCERT Solutions provide detailed answers to all textbook questions, helping students understand concepts thoroughly. They explain each step logically, making it easier to learn formulas, set operations, and problem-solving techniques. Students can use these solutions for homework, revision, and exam preparation. Regular practice improves accuracy and confidence while solving mathematical problems. Since many school examination questions are based directly on NCERT exercises, mastering these solutions can significantly improve performance. They also help students identify common mistakes and develop a deeper understanding of the chapter, which is beneficial for both school exams and future competitive examinations.
Venn diagrams are graphical representations used to show relationships among sets. They make it easier to understand operations such as union, intersection, and difference of sets. In Chapter 1 Sets, Venn diagrams help students visualize how elements are distributed within different sets. They simplify complex problems and improve accuracy while solving questions. NCERT Solutions include several examples where Venn diagrams are used to explain concepts clearly. Regular practice of these diagrams helps students quickly identify relationships among sets and solve examination questions more efficiently. Venn diagrams are also useful in probability and logical reasoning topics studied in higher classes.
Chapter 1 introduces several types of sets, including empty sets, singleton sets, finite sets, infinite sets, equal sets, equivalent sets, and universal sets. Students also learn about subsets and proper subsets. Understanding the properties of each type of set is important because they are frequently used in mathematical reasoning and problem-solving. NCERT Solutions explain these concepts with clear examples and solved exercises. By practicing questions regularly, students can learn how to identify different types of sets and apply the concepts correctly in examinations. This knowledge is also useful for understanding advanced topics later in the Class 11 Mathematics syllabus.