Q. Which of the following relations is not a function?
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A.
R = {(1, 2), (2, 3), (3, 4)}
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B.
R = {(1, 2), (1, 3)}
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C.
R = {(2, 3), (3, 4)}
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D.
R = {(4, 5), (5, 6)}
Solution
R = {(1, 2), (1, 3)} is not a function because the input 1 maps to two different outputs.
Correct Answer: B — R = {(1, 2), (1, 3)}
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Q. Which of the following relations on the set of integers is not a function?
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A.
R1 = {(1, 2), (1, 3)}
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B.
R2 = {(2, 3), (3, 4)}
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C.
R3 = {(4, 5)}
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D.
R4 = {(5, 6), (6, 7)}
Solution
R1 is not a function because the input 1 maps to two different outputs (2 and 3).
Correct Answer: A — R1 = {(1, 2), (1, 3)}
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Q. Which of the following sets is a power set of F = {1, 2}?
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A.
{{1}, {2}}
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B.
{{}, {1}, {2}, {1, 2}}
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C.
{{1, 2}}
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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}?
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A.
{∅, {a}, {b}}
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B.
{∅, {a}, {b}, {a, b}}
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C.
{a, b}
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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}?
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A.
{1, 2, 3}
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B.
{2, 3, 4}
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C.
{1, 2, 4}
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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}?
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A.
{∅, {x}, {y}, {x, y}}
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B.
{x, y}
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C.
{∅, {x, y}}
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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}?
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A.
{{1}, {2}}
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B.
{{}, {1}, {2}, {1, 2}}
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C.
{{1, 2}}
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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}?
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A.
{1, 2}
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B.
{2, 3, 4}
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C.
{5}
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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}?
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A.
{1, 2}
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B.
{0}
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C.
{3, 4}
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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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