Sets — Previous Year Questions (Class 11 Mathematics)
Sets are collections of objects. Learn about set notation, operations (union, intersection, complement), and Venn diagrams.
TL;DR: Sets are collections of objects. Learn about set notation, operations (union, intersection, complement), and Venn diagrams.
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
Sets are collections of objects. Learn about set notation, operations (union, intersection, complement), and Venn diagrams.
Sets — Previous Year Questions with Solutions
Q (2023, 1 mark): Write set A = {x : x is a natural number and x < 10} in roster form.
Answer: A = {1, 2, 3, 4, 5, 6, 7, 8, 9}
Q (2022, 3 marks): If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, find (a) A ∪ B, (b) A ∩ B, (c) A - B
Answer: (a) A ∪ B (union: all elements in A or B or both)
A ∪ B = {1, 2, 3, 4, 5, 6}
(b) A ∩ B (intersection: common elements)
A ∩ B = {3, 4}
(c) A - B (difference: elements in A but not in B)
A - B = {1, 2}
Q (2023, 3 marks): Verify De Morgan's law: (A ∪ B)' = A' ∩ B' for A = {1, 2, 3} and B = {3, 4} with universal set U = {1, 2, 3, 4, 5}
Answer: A = {1, 2, 3}, B = {3, 4}, U = {1, 2, 3, 4, 5}
Left side: (A ∪ B)'
A ∪ B = {1, 2, 3, 4}
(A ∪ B)' = {5}
Right side: A' ∩ B'
A' = {4, 5}
B' = {1, 2, 5}
A' ∩ B' = {5}
Since (A ∪ B)' = {5} = A' ∩ B', De Morgan's law is verified ✓
Q (2021, 3 marks): In a class of 50 students, 30 play cricket, 25 play football, and 10 play both. Find: (a) students who play either cricket or football, (b) students who play neither
Answer: Let C = set of students playing cricket, F = set of students playing football
n(C) = 30, n(F) = 25, n(C ∩ F) = 10, Total = 50
(a) Students playing either cricket or football:
n(C ∪ F) = n(C) + n(F) - n(C ∩ F)
= 30 + 25 - 10 = 45 students
(b) Students playing neither:
Students playing neither = Total - n(C ∪ F)
= 50 - 45 = 5 students
Q (2022, 2 marks): If A × B = {(1,2), (1,3), (2,2), (2,3)}, find sets A and B.
Answer: Cartesian product A × B = {(a,b) : a ∈ A, b ∈ B}
From given set:
Elements with first coordinate 1: (1,2), (1,3) → 1 ∈ A
Elements with first coordinate 2: (2,2), (2,3) → 2 ∈ A
So A = {1, 2}
Elements with second coordinate 2: (1,2), (2,2) → 2 ∈ B
Elements with second coordinate 3: (1,3), (2,3) → 3 ∈ B
So B = {2, 3}
Q (2023, 3 marks): State the properties of set complement and verify A ∪ A' = U.
Answer: Complement A' = {x : x ∈ U and x ∉ A}
Properties of complement:
1. A ∪ A' = U (every element is in A or A')
2. A ∩ A' = ∅ (no element is in both A and A')
3. (A')' = A (complement of complement is original set)
4. U' = ∅ and ∅' = U
Verification of A ∪ A' = U:
Let x be any element in U.
Either x ∈ A or x ∉ A (law of excluded middle)
If x ∈ A, then x ∈ A ∪ A'
If x ∉ A, then x ∈ A', so x ∈ A ∪ A'
Therefore, every element of U is in A ∪ A'
Hence, A ∪ A' = U ✓
Frequently Asked Questions
What is the difference between subset and proper subset?
Subset (A ⊆ B): All elements of A are in B (A can equal B). Proper subset (A ⊂ B): All elements of A are in B, but A ≠ B (at least one element of B is not in A). Every set is a subset of itself, but not a proper subset of itself.
What is the power set? Calculate the power set of {1, 2}.
Power set P(A) is the set of all subsets of A. For A = {1, 2}, subsets are: ∅, {1}, {2}, {1, 2}. So P(A) = {∅, {1}, {2}, {1, 2}}. If |A| = n, then |P(A)| = 2^n. Here n=2, so |P(A)| = 4.
More Class 11 Mathematics PYQs
🤖 Stuck on any of these? Ask Syllab's free AI Tutor to explain step by step →