Q. Which of the following options best exemplifies a constraint-based set?
A.
The set of all even numbers.
B.
The set of all prime numbers.
C.
The set of all integers greater than 10.
D.
The set of all colors in a rainbow.
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Solution
The set of all integers greater than 10 is a clear example of a constraint-based set, as it specifies a condition that elements must meet.
Correct Answer:
C
— The set of all integers greater than 10.
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Q. Which of the following options best illustrates a constraint-based set?
A.
The set of all even numbers.
B.
The set of all prime numbers.
C.
The set of all integers greater than 10.
D.
The set of all colors in a rainbow.
Show solution
Solution
The set of all integers greater than 10 is a clear example of a constraint-based set, as it imposes a specific condition on the elements.
Correct Answer:
C
— The set of all integers greater than 10.
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Q. Which of the following statements about constraint-based sets is correct?
A.
All elements in a constraint-based set must be unique.
B.
Constraints can be both inclusive and exclusive.
C.
Constraints do not affect the size of the set.
D.
All elements must be integers.
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Solution
Constraints can be both inclusive (allowing certain elements) and exclusive (disallowing others), affecting the composition of the set.
Correct Answer:
B
— Constraints can be both inclusive and exclusive.
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Q. Which of the following statements about constraint-based sets is true?
A.
All constraints are equal in importance.
B.
Constraints can be hierarchical.
C.
Constraints do not affect the outcome.
D.
Constraints are always numerical.
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Solution
Constraints can be hierarchical, meaning some constraints may take precedence over others in determining set membership.
Correct Answer:
B
— Constraints can be hierarchical.
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Q. Which of the following statements about constraints in set theory is FALSE?
A.
Constraints can be both inclusive and exclusive.
B.
Constraints can change the nature of the set.
C.
All constraints must be numerical.
D.
Constraints help in defining subsets.
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Solution
The statement that 'all constraints must be numerical' is false; constraints can be based on various properties, not just numerical.
Correct Answer:
C
— All constraints must be numerical.
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Q. Which of the following statements about the union of two sets is true?
A.
The union includes only the elements that are common to both sets.
B.
The union includes all elements from both sets, excluding duplicates.
C.
The union is only applicable to finite sets.
D.
The union can never be larger than the largest set.
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Solution
The union of two sets combines all unique elements from both sets.
Correct Answer:
B
— The union includes all elements from both sets, excluding duplicates.
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Q. Which of the following statements is true regarding the intersection of two constraint-based sets?
A.
The intersection will always contain all elements of both sets.
B.
The intersection may contain elements that satisfy the constraints of both sets.
C.
The intersection will be empty if the sets have no common elements.
D.
Both b and c are true.
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Solution
The intersection of two constraint-based sets may contain elements that satisfy the constraints of both sets, and it will be empty if there are no common elements.
Correct Answer:
D
— Both b and c are true.
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