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1.Introduction to Sets
Class 11 • Mathematics • NCERT
Introduction to Sets
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This lesson introduces the basic concept of sets as per NCERT Class 11. Students learn definitions, representations, types of sets, and cardinal numbers with simple examples and exam-focused MCQs.
Lesson Objectives
- Understand the definition of a set.
- Identify well-defined collections.
- Learn different types of sets.
- Understand cardinal number of a set.
1. What Is a Set?
A set is a well-defined collection of objects. The objects are called elements of the set.
Examples:
• Set of vowels in English alphabet
• Set of natural numbers less than 5
• Set of vowels in English alphabet
• Set of natural numbers less than 5
2. Representation of Sets
Sets can be represented in two ways:
Roster Form: Listing elements inside { }
Example: A = {1, 2, 3}
Example: A = {1, 2, 3}
Set-Builder Form: Describing elements using a property
Example: A = {x | x ∈ N and x < 4}
3. Types of Sets (NCERT)
• Empty Set: A set with no elements (∅)
• Singleton Set: A set with one element
• Finite Set: Limited number of elements
• Infinite Set: Unlimited number of elements
• Equal Sets: Sets with same elements
• Singleton Set: A set with one element
• Finite Set: Limited number of elements
• Infinite Set: Unlimited number of elements
• Equal Sets: Sets with same elements
4. Cardinal Number of a Set
The number of elements in a set is called its cardinal number.
If A = {1, 2, 3}, then n(A) = 3
Practice MCQs (NCERT)
- A well-defined collection is called a ______.
- The symbol for empty set is ______.
- The set of natural numbers less than 1 is ______.
- A set with one element is called a ______ set.
- The number of elements in a set is called its ______.
- The set {1,2,3} is ______.
- The set of natural numbers is ______.
- The set {x | x ∈ N, x < 4} is equal to ______.
- The cardinal number of ∅ is ______.
- The set of vowels has ______ elements.
- Order of elements in a set is ______.
- Repetition of elements in a set is ______.
- The set {1,1,2} is equal to ______.
- Which is not a set: collection of good students / months in a year?
- The set {x | x² = 4, x ∈ N} is ______.
- ∅ is a ______ set.
- The set {0} has ______ element(s).
- The set of integers is ______.
- n({a,e,i,o,u}) = ______.
- A set must be ______ defined.
✅ Show Answer Key
- Set
- ∅
- ∅
- Singleton
- Cardinal number
- Finite
- Infinite
- {1,2,3}
- 0
- 5
- Irrelevant
- Not allowed
- {1,2}
- Collection of good students
- {2}
- Empty
- 1
- Infinite
- 5
- Well
© Aviate Learning – Sets (NCERT Class 11)
