Q. If a set is defined as {x | x is a positive integer and x is a multiple of 3}, which of the following is NOT an element of this set?
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Solution
The number '10' is not a multiple of 3, hence it is not an element of the set.
Correct Answer:
D
— 10
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Q. If a set is defined as {x | x is a prime number less than 10}, which of the following elements is NOT in the set?
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Solution
The set includes prime numbers less than 10, which are 2, 3, 5, and 7. The number 4 is not a prime number.
Correct Answer:
D
— 4
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Q. If a set is defined as {x | x is a prime number less than 20}, which of the following elements is NOT included in the set?
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Solution
The number 4 is not a prime number, hence it is not included in the set of prime numbers less than 20.
Correct Answer:
C
— 4
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Q. If a set is defined as {x | x is a prime number less than 20}, which of the following elements is NOT included in this set?
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Solution
The number 4 is not a prime number, hence it is not included in the set of prime numbers less than 20.
Correct Answer:
C
— 4
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Q. If a set is defined as {x | x is an even number greater than 0 and less than 20}, which of the following is NOT an element of this set?
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Solution
The number 21 is not included in the set as it does not meet the criteria of being less than 20.
Correct Answer:
D
— 21
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Q. If a set is defined as {x | x is an integer and 1 ≤ x ≤ 10}, which of the following is a valid operation on this set?
A.
Adding 5 to each element.
B.
Removing all even numbers.
C.
Doubling each element.
D.
All of the above.
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Solution
All the operations listed can be validly performed on the set defined by the constraints.
Correct Answer:
D
— All of the above.
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Q. If a set is defined by the constraint of being a natural number, which of the following is included?
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Solution
1 is a natural number, while -1 and 0 are not considered natural numbers, and 2.5 is not an integer.
Correct Answer:
C
— 1
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Q. If a set is defined by the constraints 'x is a natural number and x < 10', which of the following is an element of this set?
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Solution
5 is a natural number and is less than 10, making it a valid element of the set defined by the given constraints.
Correct Answer:
B
— 5
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Q. If a set is defined by the constraints 'x is a real number and x^2 < 16', which of the following is NOT an element of this set?
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Solution
4 is not an element of the set because it does not satisfy the constraint x^2 < 16 (since 4^2 = 16).
Correct Answer:
C
— 4
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Q. If a set is defined by the constraints 'x is a real number and x^2 < 4', which of the following intervals represents this set?
A.
(-2, 2)
B.
(-4, 4)
C.
(-2, 2]
D.
[0, 2)
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Solution
The interval (-2, 2) represents all real numbers whose square is less than 4.
Correct Answer:
A
— (-2, 2)
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Q. If a set is defined by the constraints 'x is an integer and x > 5', which of the following is NOT an element of this set?
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Solution
5 is not an element of the set because it does not satisfy the constraint 'x > 5'.
Correct Answer:
C
— 5
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Q. If a set is defined by the constraints of being a vowel and a letter in the English alphabet, which of the following is an example of an element in this set?
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Solution
A is a vowel and meets the constraints of being a letter in the English alphabet.
Correct Answer:
C
— A
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Q. If a set is defined by the constraints of being both a multiple of 3 and less than 30, which of the following is an element of this set?
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Solution
9 is a multiple of 3 and less than 30, making it a valid element of the defined set.
Correct Answer:
A
— 9
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Q. If a set of students is defined by the constraint of having a GPA above 3.5, which of the following students would be included?
A.
Alice with a GPA of 3.4
B.
Bob with a GPA of 3.6
C.
Charlie with a GPA of 3.5
D.
Diana with a GPA of 3.2
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Solution
Bob is the only student with a GPA above 3.5, thus he is included in the set.
Correct Answer:
B
— Bob with a GPA of 3.6
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Q. If a task must be completed by Friday and takes 3 days, starting from Wednesday, which of the following is the latest possible start day?
A.
Monday
B.
Tuesday
C.
Wednesday
D.
Thursday
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Solution
Thursday is the latest start day as the task will then complete by Saturday, which is not allowed.
Correct Answer:
D
— Thursday
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Q. If all cats are mammals and some mammals are not dogs, which of the following statements must be true?
A.
All cats are dogs.
B.
Some cats are not dogs.
C.
All mammals are cats.
D.
Some dogs are not mammals.
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Solution
Since not all mammals are dogs, it follows that some cats, being mammals, cannot be dogs.
Correct Answer:
B
— Some cats are not dogs.
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Q. If all roses are flowers and some flowers fade quickly, which of the following statements is necessarily true?
A.
Some roses fade quickly.
B.
All flowers are roses.
C.
No roses fade quickly.
D.
Some flowers do not fade quickly.
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Solution
The statement indicates that while some flowers fade quickly, it does not apply to all, hence some must not.
Correct Answer:
D
— Some flowers do not fade quickly.
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Q. If hybrid set G is formed by the union of sets H and I, which of the following is true?
A.
Set G will have fewer elements than set H.
B.
Set G will have fewer elements than set I.
C.
Set G will have at least as many elements as the larger of set H or set I.
D.
Set G cannot contain any elements from set H.
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Solution
The union of two sets will always have at least as many elements as the larger of the two sets, including unique elements.
Correct Answer:
C
— Set G will have at least as many elements as the larger of set H or set I.
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Q. If hybrid sets are used to represent different categories of data, which of the following is a potential benefit? (2023)
A.
Increased complexity in data analysis.
B.
Reduction in data redundancy.
C.
Limited data representation.
D.
Inability to categorize data.
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Solution
Hybrid sets can help reduce redundancy by combining different categories of data into a single representation.
Correct Answer:
B
— Reduction in data redundancy.
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Q. If set A = {a, b, c} and set B = {b, c, d}, what is the hybrid set formed by the intersection of A and B?
A.
{a, b, c, d}
B.
{b, c}
C.
{a, d}
D.
{}
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Solution
The intersection of sets A and B 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 A contains 10 elements, set B contains 15 elements, and the intersection of A and B contains 5 elements, how many elements are in the union of sets A and B?
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Solution
The number of elements in the union of sets A and B is given by |A ∪ B| = |A| + |B| - |A ∩ B| = 10 + 15 - 5 = 20.
Correct Answer:
A
— 20
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Q. If set A contains 10 elements, set B contains 15 elements, and the intersection of A and B contains 5 elements, what is the number of elements in the union of sets A and B?
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Solution
The number of elements in the union of sets A and B is given by |A ∪ B| = |A| + |B| - |A ∩ B| = 10 + 15 - 5 = 20.
Correct Answer:
A
— 20
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Q. If set A contains 15 elements, set B contains 10 elements, and the intersection of A and B contains 5 elements, how many elements are in the union of sets A and B?
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Solution
The number of elements in the union of sets A and B is given by |A ∪ B| = |A| + |B| - |A ∩ B| = 15 + 10 - 5 = 20.
Correct Answer:
A
— 20
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Q. If set A contains 15 elements, set B contains 10 elements, and the intersection of A and B contains 5 elements, what is the number of elements in the union of sets A and B?
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Solution
The number of elements in the union of sets A and B is given by |A ∪ B| = |A| + |B| - |A ∩ B| = 15 + 10 - 5 = 20.
Correct Answer:
B
— 25
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Q. If set C is a hybrid set formed by combining set A and set B, which of the following is a possible characteristic of set C?
A.
Set C cannot have any elements from set A.
B.
Set C must have all elements from set B.
C.
Set C may have elements that are exclusive to either set A or set B.
D.
Set C will always be larger than both set A and set B.
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Solution
Hybrid sets can include elements that are exclusive to either of the original sets, making them versatile in composition.
Correct Answer:
C
— Set C may have elements that are exclusive to either set A or set B.
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Q. If set C is a hybrid set formed by combining set A and set B, which of the following must be true?
A.
All elements of set A are in set C.
B.
Set C cannot have more elements than set A.
C.
Set C must contain at least one element from set B.
D.
Set C is identical to set A.
Show solution
Solution
By definition, a hybrid set formed from set A and set B must include all elements from set A.
Correct Answer:
A
— All elements of set A are in set C.
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Q. If set C is defined as the set of all x such that x is a multiple of 3 and less than 15, which of the following is a member of set C?
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Solution
Both 12 and 9 are multiples of 3 and less than 15, but 12 is the first option listed.
Correct Answer:
A
— 12
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Q. If set C is defined as {x | x is an integer and x is divisible by 3}, which of the following integers is NOT a member of set C?
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Solution
The integer 10 is not divisible by 3, hence it is not a member of set C.
Correct Answer:
C
— 10
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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.
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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
Show solution
Solution
The range of values for set D is from 2 to 8, inclusive.
Correct Answer:
A
— 2 to 8
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