Class 11 Maths Chapter 1 Sets NCERT Solutions | Complete Guide with Examples & Questions
Class 11 Maths Chapter 1 Sets NCERT Solutions | Complete Guide with Examples & Questions
Class 11 Maths Chapter – Sets
Introduction
Sets are one of the most basic and important topics in mathematics. Almost every chapter in higher maths uses set concepts in some form.
A set is simply a collection of well-defined objects.
Examples:
A = {1, 2, 3, 4}
B = {a, e, i, o, u}
Basic Definitions
Set: A collection of objects
Element: Objects inside a set
Empty Set: A set with no elements → ∅
Finite Set: Limited number of elements
Infinite Set: Unlimited elements
Types of Sets
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Equal Sets: Same elements
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Equivalent Sets: Same number of elements
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Subset: A ⊆ B
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Proper Subset: A ⊂ B
Important Formulas
Number of Subsets
Union and Intersection
Complement
Venn Diagram Concept
Venn diagrams help in visual understanding of sets.
Circles represent sets and overlapping regions show common elements.
Solved NCERT Examples (Step by Step)
Example 1
Write the set of all vowels in English alphabet.
Solution:
A = {a, e, i, o, u}
Example 2
Find whether A = {1,2,3} and B = {3,2,1} are equal.
Solution:
Both sets have same elements
So, A = B
Example 3
If A = {1,2,3} and B = {2,3,4}, find A ∪ B.
Solution:
A ∪ B = {1,2,3,4}
Example 4
Find A ∩ B.
Solution:
Common elements = {2,3}
Example 5
Find number of subsets of A = {1,2,3}
Solution:
n = 3
Number of subsets = 2³ = 8
Example 6
If U = {1,2,3,4,5} and A = {2,3}, find A'
Solution:
A' = {1,4,5}
Example 7
Find A − B where A = {1,2,3} and B = {2}
Solution:
A − B = {1,3}
Example 8
Find B − A
Solution:
B − A = {} = ∅
Example 9
If n(A)=20, n(B)=15, n(A∩B)=5, find n(A∪B)
Solution:
n(A∪B) = 20 + 15 − 5 = 30
Example 10
Check whether {1,2} ⊂ {1,2,3}
Solution:
Yes, it is a proper subset
Exercise Based Practice Questions
You should practice:
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Writing sets in roster form
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Set builder form
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Union and intersection problems
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Venn diagram questions
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Complement and subset problems
15 FAQs
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