Power set - One Line Questions
1.
What is the power set of the set {∅, {∅}}? —
{{}, {∅}, {{∅}}, {∅, {∅}}}
2.
If A = {1, 2} and B = {2, 3}, what is P(A ∪ B)? —
{{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
3.
Let A = {1, 2}. Which of the following is the correct representation of P(A)? —
{{}, {1}, {2}, {1, 2}}
4.
Let A = {1, 2}. What is the power set of A, P(A)? —
{{}, {1}, {2}, {1, 2}}
5.
Which of the following sets is the power set of {1, 2}? —
{{}, {1}, {2}, {1, 2}}
6.
Let A = {x | x is an integer and 0 < x < 3}. What is P(A)? —
{{}, {1}, {2}, {1, 2}}
7.
Let A = {a}. What is P(A)? —
{{}, {a}}
8.
Let X = {apple, banana}. Which of the following represents P(X)? —
{{}, {apple}, {banana}, {apple, banana}}
9.
What is the power set of the empty set, denoted by {} or ∅? —
{∅}
10.
If A = {∅}, what is the power set P(A)? —
{{}, {∅}}
11.
Let A = {1, 2, 3}. Which of the following is NOT a subset of A? —
{1, 2, 3, 4}
12.
Let A = {a, b}. Which of the following is NOT a proper subset of A? —
{a, b}
13.
Let A = {1, 2, 3}. Which of the following is a proper subset of A? —
{1, 2}
14.
Let S = {1, 2, 3}. Which of the following is NOT an element of P(S)? —
{4}
15.
If A and B are two sets such that A ∩ B = ∅, then |P(A ∪ B)| is equal to: —
|P(A)| * |P(B)|
16.
What is the relationship between the cardinality of a set A, denoted by |A|, and the cardinality of its power set, |P(A)|? —
|P(A)| = 2^|A|
17.
What is the number of elements in the power set of a set with 0 elements? —
1
18.
If A = {1, 2, 3}, which of the following is an element of P(A)? —
{1}
19.
If A = {x | x is a prime number less than 10}, what is the number of elements in P(A)? —
16
20.
Consider the set A = {1, 2, 3, 4}. How many elements are in P(A)? —
16
21.
If P(A) has 16 elements, how many elements are in set A? —
4
22.
Consider the set C = {1, {1}}. How many elements are in the power set P(C)? —
4
23.
How many subsets does the power set of a set with 2 elements have? —
8
24.
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? —
2^k - 1
25.
If A has 3 elements, how many subsets does P(A) have? —
8
26.
What is the total number of subsets of a set containing 3 elements? —
8
27.
Let A = {apple, banana, cherry}. How many elements are in P(A)? —
8
28.
If |P(A)| = 256, what is |A|? —
8
29.
If a set has 5 elements, how many subsets does its power set contain? —
32
30.
What is the cardinality of the power set of the set of vowels in the English alphabet? —
32
31.
How many elements are there in the power set of the set {a, b, c, d, e}? —
32
32.
Let B = {a, b, c}. How many proper subsets does B have? —
7
33.
Let A = {1, 2, 3}. How many proper subsets does A have? —
7
34.
Let A = {a, b, c, d}. How many subsets does A have? —
16
35.
Let A = {a, b}. Which of the following is an element of P(A)? —
{a, b}
36.
Which of the following statements is true for any non-empty set A? —
A ∈ P(A)
37.
If A ∪ B = A ∩ B, what can be said about A and B? —
A = B
38.
Which statement is true about the power set P(A) and the set A? —
A is always an element of P(A)
39.
If A is a set, then A ∈ P(A) is true if and only if: —
A is the empty set
40.
The power set of a set A is denoted by: —
P(A)
41.
The set of all subsets of a set A is called its: —
Power set
42.
The power set of a set A is the set of all its: —
Subsets
43.
What is the cardinality of the power set of a set with cardinality m? —
2^m
44.
If a set A has n elements, how many elements does its power set P(A) contain? —
2^n
45.
If A ⊂ B, then which of the following is true regarding their power sets? —
P(A) ⊂ P(B)
46.
If |A| = n, then |P(A)| = 2^n. This formula is derived using: —
Binomial Theorem
47.
Which of the following is always an element of the power set of any set A? —
The empty set
48.
The number of subsets of a set with n elements is 2^n. This is directly related to the definition of: —
Power set
49.
If A is a finite set, is P(A) always finite? —
Yes
50.
If A is an infinite set, is P(A) always infinite? —
Yes