MATHEMATICS: CHAPTER 1 - SETS
Comprehensive Study Guide & Practice Workbook | Class 11 CBSE/NCERT
1. 📌 Introduction to Sets
Definition: A Set is a well-defined collection of objects. "Well-defined" means that
it should be possible to decide whether a particular object belongs to the collection
or not.
Notations: Sets are usually denoted by capital letters (A, B, X, Y), and their elements
are denoted by small letters (a, b, x, y).
• \( a \in A \): 'a' belongs to A
• \( b otin A \): 'b' does not belong to A
Representation of Sets
1. Roster/Tabular Form: Elements are listed within curly brackets and separated by
commas.
Example: Set of vowels, V = {a, e, i, o, u}.
2. Set-builder Form: Defining a set by a common property.
Example: V = {x : x is a vowel in English alphabet}.
2. 📌 Types of Sets
Type Description Example
Empty Set (Φ) Contains no elements. {x : x² = 4, x is odd}
Singleton Set Contains exactly one element. {0}
Finite Set Contains a definite number of elements. {1, 2, 3, 4, 5}
Infinite Set Number of elements is not finite. N = {1, 2, 3, ...}
Page 1
, Equal Sets A and B have exactly the same elements. A={1,2}, B={2,1}
Equivalent Sets Number of elements is same: n(A) = n(B). A={1,2}, B={a,b}
Page 2
Comprehensive Study Guide & Practice Workbook | Class 11 CBSE/NCERT
1. 📌 Introduction to Sets
Definition: A Set is a well-defined collection of objects. "Well-defined" means that
it should be possible to decide whether a particular object belongs to the collection
or not.
Notations: Sets are usually denoted by capital letters (A, B, X, Y), and their elements
are denoted by small letters (a, b, x, y).
• \( a \in A \): 'a' belongs to A
• \( b otin A \): 'b' does not belong to A
Representation of Sets
1. Roster/Tabular Form: Elements are listed within curly brackets and separated by
commas.
Example: Set of vowels, V = {a, e, i, o, u}.
2. Set-builder Form: Defining a set by a common property.
Example: V = {x : x is a vowel in English alphabet}.
2. 📌 Types of Sets
Type Description Example
Empty Set (Φ) Contains no elements. {x : x² = 4, x is odd}
Singleton Set Contains exactly one element. {0}
Finite Set Contains a definite number of elements. {1, 2, 3, 4, 5}
Infinite Set Number of elements is not finite. N = {1, 2, 3, ...}
Page 1
, Equal Sets A and B have exactly the same elements. A={1,2}, B={2,1}
Equivalent Sets Number of elements is same: n(A) = n(B). A={1,2}, B={a,b}
Page 2
