Mathematics · Class 11
Sets
Learn Sets with notes, examples, and practice questions.
4 sections15–25 min read6 MCQs · 2 examples
Chapter Overview
A set is well-defined when any object either belongs to it or does not — no ambiguity.
Sets are well-defined collections of objects. Class 11 builds the language of modern maths — membership, subsets, operations, and Venn diagrams — used throughout algebra and probability.
Key Definitions
- Element a ∈ A means a belongs to set A
- Subset A ⊆ B: every element of A is in B
- Power set P(A): set of all subsets; |P(A)| = 2^n if |A| = n
- Universal set U, empty set ∅
Operations
Union
A ∪ B = {x : x ∈ A or x ∈ B}
Intersection
A ∩ B = {x : x ∈ A and x ∈ B}
Difference
A − B = {x : x ∈ A, x ∉ B}
Complement
A′ = U − A
Important Laws
- De Morgan: (A ∪ B)′ = A′ ∩ B′
- De Morgan: (A ∩ B)′ = A′ ∪ B′
- n(A ∪ B) = n(A) + n(B) − n(A ∩ B)
- Disjoint sets: A ∩ B = ∅
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Example 1: Roster form
Write set of vowels in English alphabet.
- 1List elements explicitly
Answer
{a, e, i, o, u}
Example 2: Power set size
If |A| = 3, how many subsets?
- 1|P(A)| = 2³ = 8
Answer
8 subsets
Key Points to Remember
- ✓ Roster vs set-builder notation
- ✓ Venn diagrams for union/intersection
- ✓ De Morgan laws for complements
Exam Tips
- • Draw Venn for 3-set problems
- • Check if finite or infinite set
Practice MCQs — Sets
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Question 1 of 6Score: 0/0
Empty set is subset of every set?