Q. If set D is a hybrid set that includes elements from set E and set F, which of the following is a valid conclusion?
-
A.
All elements of set E are in set D.
-
B.
Set D cannot have any elements from set F.
-
C.
Set D may contain elements that are not in either set E or set F.
-
D.
Set D must be equal to the intersection of set E and set F.
Solution
Hybrid sets can include additional elements beyond those found in the original sets, allowing for greater flexibility.
Correct Answer:
C
— Set D may contain elements that are not in either set E or set F.
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Q. If set D is defined by the constraints z ≥ 2 and z ≤ 8, which of the following is the range of values for set D?
-
A.
2 to 8
-
B.
1 to 9
-
C.
0 to 10
-
D.
2 to 9
Solution
The range of values for set D is from 2 to 8, inclusive.
Correct Answer:
A
— 2 to 8
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Q. If set E = {x, y, z} and set F = {y, z, w}, what is the complement of set E with respect to the universal set U = {x, y, z, w, v}?
-
A.
{v}
-
B.
{w, v}
-
C.
{x, y, z}
-
D.
{y, z}
Solution
The complement of set E with respect to the universal set U includes all elements in U that are not in E, which is {v}.
Correct Answer:
A
— {v}
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Q. If set F contains elements {a, b, c} and set G contains elements {b, c, d}, what is the intersection of sets F and G?
-
A.
{a, b, c, d}
-
B.
{b, c}
-
C.
{a, d}
-
D.
{}
Solution
The intersection of sets F and G includes only the elements that are present in both sets, which are {b, c}.
Correct Answer:
B
— {b, c}
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Q. If set G = {1, 2, 3} and set H = {2, 3, 4}, what is the result of the difference G - H? (2023)
-
A.
{1}
-
B.
{2, 3}
-
C.
{3, 4}
-
D.
{}
Solution
The difference G - H includes elements in G that are not in H, which results in {1}.
Correct Answer:
A
— {1}
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Q. If set H contains elements {a, b, c} and set I contains elements {b, c, d}, what is the union of these two sets?
-
A.
{a, b, c}
-
B.
{b, c, d}
-
C.
{a, b, c, d}
-
D.
{a, d}
Solution
The union of sets H and I is {a, b, c, d}, which includes all unique elements from both sets.
Correct Answer:
C
— {a, b, c, d}
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Q. If set I = {1, 2, 3} and set J = {2, 3, 4}, what is the result of the operation I - J?
-
A.
{1}
-
B.
{2, 3}
-
C.
{4}
-
D.
{}
Solution
The operation I - J results in the elements of set I that are not in set J, which is {1}.
Correct Answer:
A
— {1}
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Q. If set T = {1, 2, 3} and set U = {2, 3, 4}, what is the difference T - U?
-
A.
{1}
-
B.
{2, 3}
-
C.
{4}
-
D.
{}
Solution
The difference T - U includes elements that are in set T but not in set U, which is {1}.
Correct Answer:
A
— {1}
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Q. If set T = {1, 2, 3} and set U = {2, 3, 4}, what is the hybrid set formed by the symmetric difference of T and U?
-
A.
{1, 4}
-
B.
{1, 2, 3, 4}
-
C.
{2, 3}
-
D.
{1, 2, 4}
Solution
The symmetric difference of sets T and U is {1, 4}, which includes elements that are in either set but not in both.
Correct Answer:
A
— {1, 4}
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Q. If set T = {1, 2, 3} and set U = {2, 3, 4}, what is the hybrid set formed by the intersection of T and U?
-
A.
{1, 2, 3, 4}
-
B.
{2, 3}
-
C.
{1, 4}
-
D.
{}
Solution
The hybrid set formed by the intersection of set T and set U includes only the elements that are common to both sets, which are {2, 3}.
Correct Answer:
B
— {2, 3}
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Q. If set X = {1, 2, 3} and set Y = {3, 4, 5}, what is the hybrid set formed by X and Y? (2023)
-
A.
{1, 2, 3, 4, 5}
-
B.
{3}
-
C.
{1, 2, 4, 5}
-
D.
{1, 2, 3, 4, 5, 6}
Solution
The hybrid set formed by combining sets X and Y includes all unique elements from both sets, resulting in {1, 2, 3, 4, 5}.
Correct Answer:
A
— {1, 2, 3, 4, 5}
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Q. If set X contains elements {1, 2, 3} and set Y contains elements {3, 4, 5}, what is the hybrid set formed by the union of X and Y?
-
A.
{1, 2, 3, 4, 5}
-
B.
{1, 2, 3}
-
C.
{3, 4, 5}
-
D.
{1, 2, 4, 5}
Solution
The hybrid set formed by the union of sets X and Y includes all unique elements from both sets, which are {1, 2, 3, 4, 5}.
Correct Answer:
A
— {1, 2, 3, 4, 5}
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Q. If set X contains {1, 2, 3} and set Y contains {3, 4, 5}, what is the hybrid set formed by the union of X and Y?
-
A.
{1, 2, 3, 4, 5}
-
B.
{3}
-
C.
{1, 2}
-
D.
{4, 5}
Solution
The union of set X and set Y includes all unique elements from both sets, resulting in {1, 2, 3, 4, 5}.
Correct Answer:
A
— {1, 2, 3, 4, 5}
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Q. If set X contains {1, 2, 3} and set Y contains {3, 4, 5}, what is the hybrid set formed by the union of set X and set Y?
-
A.
{1, 2, 3, 4, 5}
-
B.
{1, 2, 3}
-
C.
{3, 4}
-
D.
{1, 2, 4, 5}
Solution
The hybrid set formed by the union of set X and set Y includes all unique elements from both sets, which are {1, 2, 3, 4, 5}.
Correct Answer:
A
— {1, 2, 3, 4, 5}
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Q. If set X contains {1, 2, 3} and set Y contains {3, 4, 5}, what is the intersection of set X and set Y?
-
A.
{1, 2, 3, 4, 5}
-
B.
{3}
-
C.
{1, 2}
-
D.
{}
Solution
The intersection of set X and set Y is {3}, as it is the only element common to both sets.
Correct Answer:
B
— {3}
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Q. If T is sitting between U and V in a circular arrangement, and W is sitting opposite T, who is sitting next to V?
Solution
Since T is between U and V, U is next to V. W being opposite T does not change this adjacency.
Correct Answer:
B
— U
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Q. If T is sitting between U and V in a circular arrangement, and W is sitting opposite T, who is sitting next to U?
Solution
Since T is between U and V, the person sitting next to U must be V.
Correct Answer:
B
— V
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Q. If T is sitting next to U and V is sitting next to W, which of the following arrangements is possible?
-
A.
T U V W
-
B.
U T W V
-
C.
V T U W
-
D.
W V T U
Solution
The arrangement U T W V is valid as T is next to U and V is next to W.
Correct Answer:
B
— U T W V
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Q. If task A must be completed before task B, and task B must be completed before task C, which of the following is a correct sequence?
-
A.
C, B, A
-
B.
B, A, C
-
C.
A, C, B
-
D.
A, B, C
Solution
A, B, C is the correct sequence as it respects the order of dependencies.
Correct Answer:
D
— A, B, C
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Q. If task B cannot start until task A is completed, which of the following is a logical conclusion?
-
A.
A must be completed after B.
-
B.
B can start at the same time as A.
-
C.
B can only start after A is completed.
-
D.
A and B can be completed simultaneously.
Solution
The condition states that B cannot start until A is completed, making this the only valid conclusion.
Correct Answer:
C
— B can only start after A is completed.
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Q. If task B cannot start until task A is finished, and task C can start at the same time as task A, which of the following is true?
-
A.
B starts before A
-
B.
C starts after A
-
C.
C can start before B
-
D.
A and B can start simultaneously
Solution
C can start before B since it is only dependent on A.
Correct Answer:
C
— C can start before B
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Q. If task B must be completed after task A and before task C, which of the following sequences is valid?
-
A.
C, B, A
-
B.
A, B, C
-
C.
B, A, C
-
D.
A, C, B
Solution
The sequence A, B, C correctly places B after A and before C.
Correct Answer:
B
— A, B, C
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Q. If task C can only start after both tasks A and B are completed, which of the following is a correct statement?
-
A.
C can start before A and B.
-
B.
C can start after A or B.
-
C.
C can start only after A and B.
-
D.
C can start at the same time as A.
Solution
C's start is contingent upon the completion of both A and B, making option 3 correct.
Correct Answer:
C
— C can start only after A and B.
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Q. If task C cannot start until both tasks A and B are completed, which of the following is a valid conclusion?
-
A.
C can start before A
-
B.
C can start before B
-
C.
C can start only after A and B
-
D.
C can start simultaneously with A
Solution
C can only start after both A and B are completed, making the conclusion valid.
Correct Answer:
C
— C can start only after A and B
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Q. If task C is dependent on both tasks A and B being completed, which of the following is a correct statement?
-
A.
C can start before A and B.
-
B.
C can start after A or B.
-
C.
C can start only after A and B.
-
D.
C can start at the same time as A.
Solution
C can only start after both A and B are completed, as it is dependent on them.
Correct Answer:
C
— C can start only after A and B.
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Q. If task C must be completed before task A, and task A must be completed before task D, which of the following is a correct inference?
-
A.
C can start after A
-
B.
D can start before A
-
C.
A can start before C
-
D.
D can start only after C
Solution
D can only start after both A and C are completed, making the inference correct.
Correct Answer:
D
— D can start only after C
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Q. If task D must be completed before task E and task F can only start after task D, which of the following is true?
-
A.
E can start before D.
-
B.
F can start before E.
-
C.
D must be completed before both E and F.
-
D.
E must be completed before D.
Solution
D must be completed before both E and F, as per the given conditions.
Correct Answer:
C
— D must be completed before both E and F.
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Q. If task E can only start after tasks A and D are completed, which of the following is a correct statement regarding the scheduling of these tasks?
-
A.
E can start before A and D.
-
B.
E can start after A or D.
-
C.
E can start only after both A and D are completed.
-
D.
E can start at any time.
Solution
E can only start after both A and D are completed, as per the given condition.
Correct Answer:
C
— E can start only after both A and D are completed.
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Q. If task E cannot start until both tasks A and C are completed, which of the following statements is true?
-
A.
E can start before A
-
B.
E can start before C
-
C.
E can start after A and C
-
D.
E can start only after A or C
Solution
E can only start after both A and C are completed, making the statement true.
Correct Answer:
C
— E can start after A and C
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Q. If task E is dependent on both tasks A and D being completed, which of the following is a correct statement?
-
A.
E can start before A
-
B.
E can start before D
-
C.
E can start only after A and D
-
D.
E can start after A or D
Solution
E can only start after both A and D are completed, making this statement correct.
Correct Answer:
C
— E can start only after A and D
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