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1. Which of the following is a well-defined collection of objects?
A. The collection of all prime numbers less than 20
B. The collection of good students in a class
C. The collection of most difficult chapters in mathematics
D. The collection of talented actors in India
Answer: A. The collection of all prime numbers less than 20
Explanation: A set must be well-defined. "Prime numbers less than 20" is precise and objective, whereas "good", "difficult", or "talented" are subjective criteria.
2. The roster form of the set A = {x : x is an integer and -3 < x < 7} is:
A. {-2, -1, 0, 1, 2, 3, 4, 5, 6}
B. {-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7}
C. {-2, -1, 0, 1, 2, 3, 4, 5, 6, 7}
D. {-3, -2, -1, 0, 1, 2, 3, 4, 5, 6}
Answer: A. {-2, -1, 0, 1, 2, 3, 4, 5, 6}
Explanation: The strict inequalities -3 < x < 7 exclude both -3 and 7, listing all integers strictly between them.
3. What is the number of elements in the power set P(A) of a set A containing 4 elements?
A. 16
B. 8
C. 4
D. 32
Answer: A. 16
Explanation: If n(A) = n, then the number of subsets in the power set n(P(A)) = 2ⁿ. Here, 2⁴ = 16.
4. If set A has 3 elements, then the number of proper subsets of A is:
A. 7
B. 8
C. 6
D. 9
Answer: A. 7
Explanation: Total number of subsets is 2³ = 8. The number of proper subsets excludes the set itself, yielding 2ⁿ - 1 = 8 - 1 = 7.
5. Which of the following represents an empty (null) set?
A. {x : x is an even prime number greater than 2}
B. {x : x² = 4 and x is an integer}
C. {0}
D. {x : x is a natural number less than 5}
Answer: A. {x : x is an even prime number greater than 2}
Explanation: The only even prime number is 2. Thus, there are no even prime numbers greater than 2, making this an empty set Ø.
6. If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, then A ∪ B is:
A. {1, 2, 3, 4, 5, 6}
B. {3, 4}
C. {1, 2, 5, 6}
D. {1, 2}
Answer: A. {1, 2, 3, 4, 5, 6}
Explanation: Union (A ∪ B) combines all unique elements present in either set A or set B without duplicate entries.
7. If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, then A ∩ B is:
A. {3, 4}
B. {1, 2, 3, 4, 5, 6}
C. {1, 2}
D. {5, 6}
Answer: A. {3, 4}
Explanation: Intersection (A ∩ B) consists only of common elements belonging to both sets A and B, which are 3 and 4.
8. If A = {1, 2, 3, 4} and B = {3, 4, 5}, then the difference A - B is:
A. {1, 2}
B. {5}
C. {3, 4}
D. {1, 2, 5}
Answer: A. {1, 2}
Explanation: Set difference A - B contains all elements present in A that are not in B, which leaves {1, 2}.
9. Two sets A and B are said to be disjoint if:
A. A ∩ B = Ø
B. A ∪ B = Ø
C. A - B = Ø
D. A = B
Answer: A. A ∩ B = Ø
Explanation: Disjoint sets have no elements in common, meaning their intersection is the empty set (Ø).
10. If U = {1, 2, 3, 4, 5, 6, 7, 8, 9} and A = {2, 4, 6, 8}, then complement A' is:
A. {1, 3, 5, 7, 9}
B. {2, 4, 6, 8}
C. {1, 2, 3, 4, 5, 6, 7, 8, 9}
D. Ø
Answer: A. {1, 3, 5, 7, 9}
Explanation: The complement A' = U - A includes all elements of universal set U that are not present in A.
11. De Morgan's Law states that for any two sets A and B:
A. (A ∪ B)' = A' ∩ B'
B. (A ∪ B)' = A' ∪ B'
C. (A ∩ B)' = A' ∩ B'
D. A ∪ B = A' ∩ B'
Answer: A. (A ∪ B)' = A' ∩ B'
Explanation: According to De Morgan's Laws, the complement of the union of two sets is equal to the intersection of their individual complements.
12. If n(A) = 15, n(B) = 20, and n(A ∩ B) = 5, then n(A ∪ B) is equal to:
A. 30
B. 35
C. 40
D. 25
Answer: A. 30
Explanation: Using cardinal formula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 15 + 20 - 5 = 30.
13. The set builder form of A = {1/2, 2/3, 3/4, 4/5, 5/6} is:
A. {x : x = n/(n+1), where n ∈ N and 1 ≤ n ≤ 5}
B. {x : x = n/(n-1), where n ∈ N and 1 ≤ n ≤ 5}
C. {x : x = (n+1)/n, where n ∈ N and 1 ≤ n ≤ 5}
D. {x : x = n/2n, where n ∈ N}
Answer: A. {x : x = n/(n+1), where n ∈ N and 1 ≤ n ≤ 5}
Explanation: Substituting natural numbers n = 1, 2, 3, 4, 5 into x = n/(n+1) generates 1/2, 2/3, 3/4, 4/5, 5/6.
14. Which of the following is a finite set?
A. The set of months in a year
B. The set of lines parallel to the x-axis
C. The set of prime numbers
D. The set of points on a line segment
Answer: A. The set of months in a year
Explanation: A finite set contains a countable number of elements; a year contains exactly 12 months.
15. The interval representation of {x ∈ R : -4 < x ≤ 6} is:
A. (-4, 6]
B. [-4, 6]
C. (-4, 6)
D. [-4, 6)
Answer: A. (-4, 6]
Explanation: Strict inequality (-4 < x) uses an open parenthesis '(', while non-strict inequality (x ≤ 6) uses a closed bracket ']'.
16. If set A = Ø (empty set), then the cardinal number of P(P(A)) is:
A. 2
B. 1
C. 0
D. 4
Answer: A. 2
Explanation: For A = Ø, n(A) = 0. Then n(P(A)) = 2⁰ = 1. Consequently, n(P(P(A))) = 2¹ = 2.
17. For any set A, (A')' is equal to:
A. A
B. A'
C. U
D. Ø
Answer: A. A
Explanation: The Law of Double Complementation states that taking the complement of a complement yields the original set A.
18. The symmetric difference of two sets A and B, denoted by A Δ B, is defined as:
A. (A - B) ∪ (B - A)
B. (A ∩ B) - (A ∪ B)
C. (A - B) ∩ (B - A)
D. (A ∪ B) ∩ (A ∩ B)
Answer: A. (A - B) ∪ (B - A)
Explanation: Symmetric difference contains elements belonging to set A or set B, but not to both simultaneously.
19. In a group of 50 people, 30 like tea, 25 like coffee, and 10 like both. How many like neither tea nor coffee?
A. 5
B. 10
C. 15
D. 20
Answer: A. 5
Explanation: n(T ∪ C) = 30 + 25 - 10 = 45. People who like neither = Total - n(T ∪ C) = 50 - 45 = 5.
20. If A ⊂ B, then A ∩ B is equal to:
A. A
B. B
C. Ø
D. U
Answer: A. A
Explanation: When A is a subset of B, every element of A is inside B, so their common elements form set A.
21. If A ⊂ B, then A ∪ B is equal to:
A. B
B. A
C. Ø
D. A ∩ B
Answer: A. B
Explanation: Since set B contains all elements of set A, combining both sets in union simply yields set B.
22. Which of the following is correct regarding Universal set U and empty set Ø?
A. U' = Ø and Ø' = U
B. U' = U and Ø' = Ø
C. U' = U and Ø' = U
D. U' = Ø and Ø' = Ø
Answer: A. U' = Ø and Ø' = U
Explanation: By law of empty set and universal set, the complement of universal set is empty set and vice versa.
23. If set A has m elements and set B has n elements, then total number of subsets of A × B is:
A. 2ᵐⁿ
B. 2ᵐ⁺ⁿ
C. m × n
D. 2ᵐ
Answer: A. 2ᵐⁿ
Explanation: Number of elements in Cartesian product n(A × B) = m × n. Total subsets of A × B = 2ᵐⁿ.
24. What is the number of elements in set A if A = {x : x ∈ R, x² = -1}?
A. 0
B. 1
C. 2
D. Infinite
Answer: A. 0
Explanation: No real number squared produces a negative value (-1). Thus, set A contains 0 elements (empty set).
25. For any sets A and B, A ∩ (A ∪ B) is equal to:
A. A
B. B
C. Ø
D. A ∪ B
Answer: A. A
Explanation: By the Absorption Law of set operations, intersecting set A with its union with B returns set A.
26. If A = {x : x is a letter in the word "ALLOY"} and B = {x : x is a letter in the word "LOYAL"}, then:
A. A = B
B. A ⊂ B and A ≠ B
C. A and B are disjoint
D. A ∩ B = Ø
Answer: A. A = B
Explanation: In roster form, A = {A, L, O, Y} and B = {L, O, Y, A}. Repetition does not change set equality, so A = B.
27. If n(U) = 700, n(A) = 200, n(B) = 300 and n(A ∩ B) = 100, then n(A' ∩ B') is:
This page contains a chapter-wise objective practice set. Try the questions without checking the answer first, then use the explanation to understand the point you missed. The current page contains 30 questions, so you can practise in smaller sets when you are revising.
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