Q. What is the number of proper subsets of the set E = {a, b}?
Solution
The total number of subsets is 2^n = 2^2 = 4. Proper subsets exclude the set itself, so there are 4 - 1 = 3 proper subsets.
Correct Answer: B — 3
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Q. What is the number of subsets of the empty set?
Solution
The empty set has exactly one subset, which is itself (∅).
Correct Answer: B — 1
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Q. What is the number of subsets of the set F = {x, y, z}?
Solution
The number of subsets of a set with n elements is 2^n. Here, n = 3, so 2^3 = 8.
Correct Answer: D — 8
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Q. What is the number of subsets of the set H = {1, 2, 3, 4, 5}?
Solution
The number of subsets of a set with n elements is 2^n. Here, n = 5, so 2^5 = 32.
Correct Answer: A — 32
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Q. What is the number of subsets of the set H = {x, y, z, w, v}?
Solution
The number of subsets of a set with n elements is 2^n. Here, n = 5, so the number of subsets is 2^5 = 32.
Correct Answer: A — 32
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Q. What is the number of subsets of the set {1, 2, 3, 4}?
Solution
The number of subsets of a set with n elements is 2^n. Here, n = 4, so the number of subsets is 2^4 = 16.
Correct Answer: C — 16
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Q. What is the power set of the empty set ∅?
-
A.
{∅}
-
B.
{∅, {∅}}
-
C.
∅
-
D.
{∅, ∅}
Solution
The power set of the empty set contains only the empty set itself: {∅}.
Correct Answer: A — {∅}
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Q. What is the power set of the set F = {a}?
-
A.
{∅, {a}}
-
B.
{∅, a}
-
C.
{a}
-
D.
{∅}
Solution
The power set of F = {a} is {∅, {a}}.
Correct Answer: A — {∅, {a}}
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Q. What is the power set of the set G = {1}?
-
A.
{∅, {1}}
-
B.
{1}
-
C.
{∅}
-
D.
{1, ∅}
Solution
The power set of G = {1} is {∅, {1}}.
Correct Answer: A — {∅, {1}}
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Q. What is the power set of the set {1, 2}?
-
A.
{∅, {1}, {2}, {1, 2}}
-
B.
{∅, {1, 2}}
-
C.
{1, 2}
-
D.
{1, 2, ∅}
Solution
The power set of a set with n elements has 2^n elements. For {1, 2}, the power set is {∅, {1}, {2}, {1, 2}}.
Correct Answer: A — {∅, {1}, {2}, {1, 2}}
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Q. What is the total number of subsets of the empty set?
Solution
The empty set has exactly one subset, which is itself: ∅.
Correct Answer: B — 1
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Q. What is the total number of subsets of the set G = {1, 2, 3, 4, 5}?
Solution
The total number of subsets is 2^5 = 32.
Correct Answer: A — 32
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Q. What is the union of the sets I = {1, 2} and J = {2, 3}?
-
A.
{1, 2, 3}
-
B.
{1, 2}
-
C.
{2, 3}
-
D.
{1, 2, 2, 3}
Solution
The union of two sets includes all unique elements from both sets. Thus, I ∪ J = {1, 2, 3}.
Correct Answer: A — {1, 2, 3}
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Q. What is the union of the sets {1, 2} and {2, 3}?
-
A.
{1, 2}
-
B.
{1, 2, 3}
-
C.
{2, 3}
-
D.
{1, 2, 2, 3}
Solution
The union of two sets includes all elements from both sets without duplicates. Thus, {1, 2} ∪ {2, 3} = {1, 2, 3}.
Correct Answer: B — {1, 2, 3}
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Q. What is the union of the sets {a, b} and {b, c}?
-
A.
{a, b}
-
B.
{a, b, c}
-
C.
{b, c}
-
D.
{a, c}
Solution
The union of two sets is the set of elements that are in either set. Here, {a, b} ∪ {b, c} = {a, b, c}.
Correct Answer: B — {a, b, c}
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Q. Which of the following is a subset of {1, 2, 3}?
-
A.
{1, 2}
-
B.
{4}
-
C.
{1, 2, 3, 4}
-
D.
{2, 3, 4}
Solution
A subset is a set that contains elements from another set. {1, 2} is a subset of {1, 2, 3}.
Correct Answer: A — {1, 2}
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Q. Which of the following is a subset of {x, y, z}?
-
A.
{x, y}
-
B.
{x, y, z, w}
-
C.
{y, z, w}
-
D.
{x, y, z, x}
Solution
A subset can only contain elements that are in the original set. {x, y} is a valid subset of {x, y, z}.
Correct Answer: A — {x, y}
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Q. Which of the following is not a subset of {a, b, c}?
-
A.
{a}
-
B.
{b, c}
-
C.
{a, b, c}
-
D.
{d}
Solution
The set {d} does not contain any elements from {a, b, c}, so it is not a subset.
Correct Answer: D — {d}
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Q. Which of the following sets is a power set of F = {1, 2}?
-
A.
{{1}, {2}}
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B.
{{}, {1}, {2}, {1, 2}}
-
C.
{{1, 2}}
-
D.
{{1, 2}, {1}}
Solution
The power set of F = {1, 2} is {{}, {1}, {2}, {1, 2}}.
Correct Answer: B — {{}, {1}, {2}, {1, 2}}
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Q. Which of the following sets is a power set of F = {a, b}?
-
A.
{∅, {a}, {b}}
-
B.
{∅, {a}, {b}, {a, b}}
-
C.
{a, b}
-
D.
{a, b, ∅}
Solution
The power set of F = {a, b} is {∅, {a}, {b}, {a, b}}.
Correct Answer: B — {∅, {a}, {b}, {a, b}}
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Q. Which of the following sets is a universal set for the sets A = {1, 2} and B = {2, 3}?
-
A.
{1, 2, 3}
-
B.
{2, 3, 4}
-
C.
{1, 2, 4}
-
D.
{1, 3}
Solution
A universal set contains all elements under consideration. Here, {1, 2, 3} contains all elements from both A and B.
Correct Answer: A — {1, 2, 3}
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Q. Which of the following sets is equal to the power set of G = {x, y}?
-
A.
{∅, {x}, {y}, {x, y}}
-
B.
{x, y}
-
C.
{∅, {x, y}}
-
D.
{x, y, ∅}
Solution
The power set of a set with n elements has 2^n subsets. For G, n=2, so the power set is {∅, {x}, {y}, {x, y}}.
Correct Answer: A — {∅, {x}, {y}, {x, y}}
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Q. Which of the following sets is equal to the set of all subsets of {1, 2}?
-
A.
{{1}, {2}}
-
B.
{{}, {1}, {2}, {1, 2}}
-
C.
{{1, 2}}
-
D.
{{1, 2}, {1}, {2}}
Solution
The power set of {1, 2} is {{}, {1}, {2}, {1, 2}}.
Correct Answer: B — {{}, {1}, {2}, {1, 2}}
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Q. Which of the following sets is not a subset of {1, 2, 3, 4}?
-
A.
{1, 2}
-
B.
{2, 3, 4}
-
C.
{5}
-
D.
{1, 2, 3}
Solution
A subset can only contain elements from the original set. {5} is not a subset of {1, 2, 3, 4}.
Correct Answer: C — {5}
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Q. Which of the following sets is not a subset of {x | x is a natural number}?
-
A.
{1, 2}
-
B.
{0}
-
C.
{3, 4}
-
D.
{5, 6}
Solution
The set {0} is not a subset of the natural numbers, as natural numbers start from 1.
Correct Answer: B — {0}
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