CBSE · Class 11 · Mathematics · Chapter 1

Chapter 1:
Sets

Complete chapter resources for CBSE Class 11 Mathematics — topic breakdown, key formulas, sample questions, previous year board questions, and instant AI question paper generation.

4Topics
6–8Board marks
8Sample questions
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Key Formulas & Concepts — Chapter 1
  • Union: n(A ∪ B) = n(A) + n(B) − n(A ∩ B)
  • Complement: A' = U − A; n(A') = n(U) − n(A)
  • Power set: |P(A)| = 2ⁿ (n = |A|)
  • De Morgan's Law: (A ∪ B)' = A' ∩ B'
  • 3-set inclusion: n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A ∩ B) − n(B ∩ C) − n(A ∩ C) + n(A ∩ B ∩ C)
  • Subset count: A set of n elements has 2ⁿ subsets and (2ⁿ − 1) proper subsets
Chapter Overview

What this chapter covers

A set is a well-defined collection of distinct objects, called its elements or members. Chapter 1 introduces the language of sets — roster (tabular) form, set-builder form, and the standard symbols (∈, ∉, ⊆, ⊂, ∅). Students learn to classify sets as empty, finite, infinite, equal, or equivalent, and understand the concept of a universal set that contains all objects relevant to a given discussion.

The chapter builds on this foundation with set operations: union (A ∪ B), intersection (A ∩ B), difference (A − B), and complement (A'). These operations are visualised using Venn diagrams, which provide a powerful pictorial tool for solving word problems. Key algebraic laws — commutative, associative, distributive, and De Morgan's laws — allow students to simplify complex set expressions without enumeration.

The inclusion-exclusion principle — n(A ∪ B) = n(A) + n(B) − n(A ∩ B) and its three-set extension — is the most examination-critical result of the chapter. Board word problems routinely present survey data (e.g., students who like Cricket, Football, or both) and ask for counts using this formula. Mastery here directly translates into 4–5 guaranteed marks in the board exam.

Topics

What's inside Chapter 1

As per NCERT Class 11 Mathematics (CBSE syllabus)

Topic 1
Sets and Their Representations
Definition of a set. Roster (tabular) form and set-builder form. Types of sets: empty, finite, infinite, equal, and equivalent sets. Concept of a universal set.
Topic 2
Subsets and Power Sets
Subsets (A ⊆ B) and proper subsets (A ⊂ B). Intervals as subsets of real numbers. Power set P(A) and the result that P(A) has 2ⁿ elements for a set with n elements.
Topic 3
Venn Diagrams and Set Operations
Union (A ∪ B), intersection (A ∩ B), difference (A − B), and complement (A'). Venn diagram representation. Laws: commutative, associative, distributive, identity, De Morgan's.
Topic 4
Practical Problems using Sets
Inclusion-exclusion principle: n(A ∪ B) = n(A) + n(B) − n(A ∩ B) and its three-set version. Survey-based word problems using cardinal number formulas.
Connections

How this chapter fits in

Useful for setting question difficulty and cross-chapter papers.

Builds on
Class 10 · Number Systems
Natural numbers, integers, rationals, irrationals — all become sets in Class 11
Class 10 · Basic Logic
AND / OR / NOT logic maps directly to intersection, union, and complement
Chapter 1 Sets
Leads to
Ch 2 · Relations & Functions
Cartesian product, domain, codomain, and range are all built on set language
Class 12 · Probability
Sample space, events, union, and intersection of events use set operations throughout
Board Blueprint

Marks & question-type breakdown

Typical pattern based on CBSE Class 11 Maths board papers from the last five years.

Question type Marks Typical count What's usually tested
MCQ / Assertion-Reason 1 1–2 Power set size, identifying subset relationships, or De Morgan's law
Very Short Answer 2 1 List subsets, write set-builder form, find A − B or A ∩ B from given sets
Short Answer 3 1 Venn diagram-based proof of a set identity or a two-set cardinal problem
Long Answer / Word Problem 4–5 1 Three-set inclusion-exclusion survey problem with full working
Total (approximate) 6–8 4–5 Part of the Sets and Functions unit (~23 marks); weightage varies by paper set
Sample Questions

8 sample questions — generated by MarksZen AI

Aligned to CBSE Class 11 Maths Chapter 1. Covers all question types across Easy, Medium, and Hard difficulty.

Q1 Easy 1 mark MCQ
If A = {1, 2, 3, 4}, the number of subsets of A is: (a) 8 (b) 12 (c) 16 (d) 32
Q2 Easy 2 marks Short Answer
Write the set A = {x : x is a vowel in the English alphabet} in roster form. Also find n(A).
Q3 Medium 2 marks Short Answer
If A = {1, 2, 3, 5, 7} and B = {3, 5, 7, 9, 11}, find A ∪ B, A ∩ B, and A − B.
Q4 Medium 3 marks Short Answer
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {2, 4, 6, 8}, and B = {3, 6, 9}. Verify De Morgan's law: (A ∪ B)' = A' ∩ B'.
Q5 Medium 3 marks Short Answer
If A and B are two sets such that n(A) = 17, n(B) = 23, and n(A ∪ B) = 35, find n(A ∩ B) and draw a Venn diagram representing the situation.
Q6 Hard 4 marks Word Problem
In a class of 60 students, 35 play cricket, 30 play football, and 10 play both cricket and football. Using the inclusion-exclusion principle: (i) Find how many students play at least one sport. (ii) Find how many students play neither cricket nor football.
Q7 Hard 5 marks Word Problem
In a survey of 100 students: 60 read Hindi newspaper, 40 read English newspaper, and 20 read both. A student is selected at random. (i) How many read neither Hindi nor English newspaper? (ii) How many read only Hindi? (iii) How many read only English? Illustrate with a Venn diagram.
Q8 Hard 5 marks Case-Based
In a group of 65 people, 40 like cricket, 10 like both cricket and tennis, and 25 like tennis. (i) How many like cricket or tennis? (ii) How many like cricket only? (iii) How many like tennis only? (iv) Verify using the formula n(A ∪ B) = n(A) + n(B) − n(A ∩ B).
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Previous Year Questions

From CBSE board examinations

Actual questions from past Class 11 Maths board papers — Sets chapter.

Board 20222 marks
If A = {3, 5, 7, 9, 11} and B = {7, 9, 11, 13}, find A ∩ B and (A ∩ B)'. Also write n(A ∩ B). (CBSE 2022)
Board 20234 marks
In a survey it was found that 21 people liked product A, 26 people liked product B and 29 people liked product C. If 14 people liked products A and B, 12 people liked products C and A, 14 people liked products B and C and 8 liked all three products, find how many liked product C only. (All India 2023)
Board 20203 marks
If A and B are two sets such that A ∪ B has 18 elements, A has 8 elements and B has 15 elements, how many elements does A ∩ B have? Also find n(A − B) and n(B − A). (CBSE 2020)
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FAQ

Questions teachers ask

How many marks does Sets carry in the CBSE Class 11 Mathematics board exam? +
Typically 6–8 marks across 3–4 questions — one 1-mark MCQ or assertion-reason item, one 2-mark short answer on set operations or Venn diagrams, and one 4–5 mark problem using the inclusion-exclusion principle. Sets appears in CBSE Class 11 Maths papers as part of the Sets and Functions unit, which carries about 23 marks in total.
What is the difference between a subset and a proper subset in CBSE exams? +
A is a subset of B (A ⊆ B) if every element of A is also in B — this includes the case where A equals B. A is a proper subset of B (A ⊂ B) if A ⊆ B and A ≠ B, meaning B has at least one element not in A. Board questions frequently ask students to list all subsets of a small set and count them using the formula 2ⁿ, where n is the number of elements.
How is the inclusion-exclusion principle applied in board questions? +
The formula n(A ∪ B) = n(A) + n(B) − n(A ∩ B) is the most commonly tested result from this chapter. Board word problems give you two or three of these values and ask for the fourth. For three sets: n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A ∩ B) − n(B ∩ C) − n(A ∩ C) + n(A ∩ B ∩ C). These problems typically appear as 4–5 mark long-answer questions.
What are the types of sets students must know for the CBSE Class 11 exam? +
Students must know: Empty set (∅ or {}), Finite and Infinite sets, Equal sets, Subsets and Power sets, Universal set, and Disjoint sets. Venn diagram-based questions frequently test whether two sets are disjoint, overlapping, or one is a subset of the other. The power set concept (P(A) has 2ⁿ elements) is a recurring 1–2 mark question.
How do I generate a custom question paper for Sets using MarksZen? +
Sign up for a free MarksZen account, choose CBSE Class 11 Mathematics, select Chapter 1 (Sets), set your preferred question-type mix (MCQ, short answer, word problem) and total marks — the AI generates a complete board-aligned paper with answer key in under 2 minutes, ready for PDF export.