Power set - Question Bank

1. Let A = {a, b}. Which of the following is NOT a proper subset of A?
A) {}
B) {a}
C) {b}
D) {a, b}
2. How many subsets does the power set of a set with 2 elements have?
A) 2
B) 4
C) 8
D) 16
3. Which of the following statements is true for any non-empty set A?
A) A ∈ P(A)
B) A ⊂ P(A)
C) A = P(A)
D) ∅ ∈ A
4. If A = {1, 2, 3}, which of the following is an element of P(A)?
A) 1
B) {1}
C) {1, 2, 3, 4}
D) ∅
5. The power set of a set A is denoted by:
A) A'
B) P(A)
C) A^c
D) A*
6. Let A = {apple, banana, cherry}. How many elements are in P(A)?
A) 3
B) 6
C) 8
D) 9
7. If |A| = n, then |P(A)| = 2^n. This formula is derived using:
A) Permutations
B) Combinations
C) Binomial Theorem
D) Principle of Inclusion-Exclusion
8. Let A = {1, 2}. Which of the following is the correct representation of P(A)?
A) {{}, {1}, {2}}
B) {{1}, {2}, {1, 2}}
C) {{}, {1}, {2}, {1, 2}}
D) {{1, 2}}
9. What is the total number of subsets of a set containing 3 elements?
A) 3
B) 6
C) 8
D) 9
10. If A is a set, then A ∈ P(A) is true if and only if:
A) A is the empty set
B) A is a singleton set
C) A is a finite set
D) A is an infinite set
11. Let A = {1, 2, 3}. Which of the following is NOT a subset of A?
A) {}
B) {1, 2}
C) {1, 2, 3, 4}
D) {2, 3}
12. How many elements are there in the power set of the set {a, b, c, d, e}?
A) 5
B) 10
C) 25
D) 32
13. If A = {1, 2} and B = {2, 3}, what is P(A ∪ B)?
A) {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
B) {{}, {1}, {2}, {3}}
C) {{}, {1, 2}, {2, 3}, {1, 2, 3}}
D) {{}, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 2, 3}}
14. Let A = {a, b}. Which of the following is an element of P(A)?
A) a
B) {a, b}
C) {{a}}
D) b
15. What is the cardinality of the power set of the set of vowels in the English alphabet?
A) 5
B) 10
C) 25
D) 32
16. If A is an infinite set, is P(A) always infinite?
A) Yes
B) No
C) Only if A is countably infinite
D) Only if A is uncountably infinite
17. Let A = {x | x is an integer and 0 < x < 3}. What is P(A)?
A) {{1}, {2}}
B) {{1, 2}}
C) {{}, {1}, {2}, {1, 2}}
D) {{}, {1}, {2}}
18. The number of subsets of a set with n elements is 2^n. This is directly related to the definition of:
A) Union
B) Intersection
C) Power set
D) Cartesian product
19. Consider the set A = {1, 2, 3, 4}. How many elements are in P(A)?
A) 16
B) 32
C) 64
D) 256
20. If A ∪ B = A ∩ B, what can be said about A and B?
A) A ⊂ B
B) B ⊂ A
C) A = B
D) A and B are disjoint
21. What is the power set of the set {∅, {∅}}?
A) {{}, {∅}, {{∅}}}
B) {{∅}, {{∅}}}
C) {{}, {∅}, {∅, {∅}}}
D) {{}, {∅}, {{∅}}, {∅, {∅}}}
22. Let A = {1, 2, 3}. How many proper subsets does A have?
A) 7
B) 8
C) 6
D) 3
23. If a set has 5 elements, how many subsets does its power set contain?
A) 5
B) 10
C) 25
D) 32
24. Which of the following sets is the power set of {1, 2}?
A) {{1}, {2}}
B) {{1, 2}}
C) {{}, {1}, {2}, {1, 2}}
D) {{1}, {2}, {1, 2}}
25. If A and B are two sets such that A ∩ B = ∅, then |P(A ∪ B)| is equal to:
A) |P(A)| + |P(B)|
B) |P(A)| * |P(B)|
C) |P(A)| + |P(B)| - 1
D) |P(A)| * |P(B)| - 1
26. Let A = {a}. What is P(A)?
A) {{a}}
B) {{}, {a}}
C) {{}, {}, {a}}
D) {{}, a}
27. The set of all subsets of a set A is called its:
A) Complement
B) Union
C) Power set
D) Intersection
28. If |P(A)| = 256, what is |A|?
A) 4
B) 8
C) 16
D) 32
29. Let A = {1, 2, 3}. Which of the following is a proper subset of A?
A) {1, 2, 3}
B) {1, 4}
C) {1, 2}
D) {{1, 2}}
30. Which statement is true about the power set P(A) and the set A?
A) A is always an element of P(A)
B) A is always a subset of P(A)
C) A is always equal to P(A)
D) A is never a subset of P(A)
31. If A has 3 elements, how many subsets does P(A) have?
A) 3
B) 6
C) 8
D) 9
32. What is the cardinality of the power set of a set with cardinality m?
A) m
B) 2m
C) m^2
D) 2^m
33. Let X = {apple, banana}. Which of the following represents P(X)?
A) {{apple}, {banana}}
B) {{apple, banana}}
C) {{}, {apple}, {banana}, {apple, banana}}
D) {{}, {apple, banana}}
34. If A = {x | x is a prime number less than 10}, what is the number of elements in P(A)?
A) 16
B) 32
C) 64
D) 128
35. What is the number of elements in the power set of a set with 0 elements?
A) 0
B) 1
C) 2
D) Undefined
36. Let S = {1, 2, 3}. Which of the following is NOT an element of P(S)?
A) {1, 2}
B) {4}
C) {}
D) {1, 2, 3}
37. If A is a finite set, is P(A) always finite?
A) Yes
B) No
C) Only if A is empty
D) Only if A has more than one element
38. The power set of a set A is the set of all its:
A) Elements
B) Proper subsets
C) Subsets
D) Supersets
39. Let A = {a, b, c, d}. How many subsets does A have?
A) 8
B) 12
C) 16
D) 32
40. If A ⊂ B, then which of the following is true regarding their power sets?
A) P(A) ⊂ P(B)
B) P(B) ⊂ P(A)
C) P(A) = P(B)
D) P(A) ∩ P(B) = ∅
41. What is the relationship between the cardinality of a set A, denoted by |A|, and the cardinality of its power set, |P(A)|?
A) |P(A)| = |A|
B) |P(A)| = 2 * |A|
C) |P(A)| = |A|^2
D) |P(A)| = 2^|A|
42. Consider the set C = {1, {1}}. How many elements are in the power set P(C)?
A) 2
B) 3
C) 4
D) 5
43. If A = {∅}, what is the power set P(A)?
A) {}
B) {{∅}}
C) {{}, {∅}}
D) {{}, {∅}, {∅, ∅}}
44. A proper subset of a set A is a subset of A that is not equal to A. If a set has k elements, how many proper subsets does it have?
A) 2^k
B) 2^k - 1
C) 2^k - 2
D) k
45. Let B = {a, b, c}. How many proper subsets does B have?
A) 7
B) 8
C) 6
D) 3
46. Which of the following is always an element of the power set of any set A?
A) The set A itself
B) The empty set
C) A set containing only the elements of A
D) A set with one more element than A
47. If P(A) has 16 elements, how many elements are in set A?
A) 2
B) 4
C) 8
D) 16
48. Let A = {1, 2}. What is the power set of A, P(A)?
A) {{1}, {2}}
B) {{1, 2}}
C) {{}, {1}, {2}, {1, 2}}
D) {{}, {1, 2}}
49. What is the power set of the empty set, denoted by {} or ∅?
A) {}
B) {∅}
C) {{}}
D) ∅
50. If a set A has n elements, how many elements does its power set P(A) contain?
A) n
B) 2n
C) n^2
D) 2^n
All Question Banks
E-Book Power set One Line Questions Power set Online Test Power set