Q. If a government decides to allocate more resources to education rather than healthcare, which of the following best describes this decision?
A.
A trade-off.
B.
An investment.
C.
A misallocation.
D.
A balanced approach.
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Solution
The decision to allocate more resources to one sector over another represents a trade-off, making option 0 the correct choice.
Correct Answer:
A
— A trade-off.
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Q. If a government decides to allocate more resources to public health rather than education, this decision can be seen as prioritizing: (2023)
A.
Short-term benefits over long-term investments.
B.
Equity over efficiency.
C.
Economic growth over social welfare.
D.
Immediate needs over future needs.
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Solution
Allocating more resources to public health reflects a focus on immediate needs, making option 3 the correct choice.
Correct Answer:
D
— Immediate needs over future needs.
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Q. If a hybrid set contains elements from both set X and set Y, which of the following is a valid conclusion?
A.
All elements of set X are in the hybrid set.
B.
All elements of set Y are in the hybrid set.
C.
Some elements of set X may not be in the hybrid set.
D.
The hybrid set cannot contain elements from both sets.
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Solution
It is possible for some elements of set X to not be included in the hybrid set, as hybrid sets can vary in composition.
Correct Answer:
C
— Some elements of set X may not be in the hybrid set.
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Q. If a hybrid set contains elements from three different categories, which of the following is a valid inference?
A.
All elements belong to the same category.
B.
At least one element must belong to each category.
C.
No elements can belong to more than one category.
D.
The categories must be mutually exclusive.
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Solution
In a hybrid set with elements from different categories, at least one element must belong to each category.
Correct Answer:
B
— At least one element must belong to each category.
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Q. If a hybrid set contains elements from three different sets, what can be inferred about its composition?
A.
It must contain at least one element from each set.
B.
It can only contain elements from the largest set.
C.
It will have no duplicates.
D.
It can include elements that are not in any of the three sets.
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Solution
A hybrid set formed from multiple sets typically includes at least one element from each contributing set.
Correct Answer:
A
— It must contain at least one element from each set.
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Q. If a hybrid set contains elements from three different sets, what can be inferred about its size compared to the individual sets? (2023)
A.
It will always be smaller than the smallest set.
B.
It can be larger than the sum of the sizes of the individual sets.
C.
It will be equal to the largest set.
D.
It can be smaller than the sum of the sizes of the individual sets.
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Solution
The size of a hybrid set can vary and may be smaller than the sum of the sizes of the individual sets due to overlapping elements.
Correct Answer:
D
— It can be smaller than the sum of the sizes of the individual sets.
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Q. If a hybrid set contains elements from three different sets, which of the following is a possible characteristic of this hybrid set?
A.
It can only contain elements from two of the sets.
B.
It must contain all elements from each of the three sets.
C.
It may contain elements that are common to all three sets.
D.
It cannot have any elements that are unique to one set.
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Solution
A hybrid set can include elements that are common to all three sets, as well as unique elements.
Correct Answer:
C
— It may contain elements that are common to all three sets.
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Q. If a hybrid set contains elements {x, y, z} and another set contains {y, z, w}, what is the hybrid set's complement with respect to the universal set {x, y, z, w, v}?
A.
{v}
B.
{x, w}
C.
{y, z}
D.
{x, y, z, w}
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Solution
The complement of the hybrid set with respect to the universal set includes elements that are in the universal set but not in the hybrid set, which is {v}.
Correct Answer:
A
— {v}
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Q. If a hybrid set is created from set T = {1, 2} and set U = {2, 3, 4}, what is the resulting hybrid set?
A.
{1, 2, 3, 4}
B.
{2}
C.
{1, 3, 4}
D.
{1, 2, 4}
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Solution
The hybrid set formed by the union of set T and set U includes all unique elements from both sets, which are {1, 2, 3, 4}.
Correct Answer:
A
— {1, 2, 3, 4}
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Q. If a hybrid set is defined as A ∪ B, which of the following is true?
A.
It includes all elements from A and B.
B.
It includes only the common elements of A and B.
C.
It includes elements from A but not from B.
D.
It includes elements from B but not from A.
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Solution
The union of sets A and B includes all elements from both sets, regardless of whether they are common or unique.
Correct Answer:
A
— It includes all elements from A and B.
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Q. If a hybrid set is defined as the combination of set R = {x, y} and set S = {y, z}, what is the resulting hybrid set?
A.
{x, y, z}
B.
{y, z}
C.
{x, y}
D.
{x, y, y, z}
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Solution
The resulting hybrid set is {x, y, z}, which includes all unique elements from both sets.
Correct Answer:
A
— {x, y, z}
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Q. If a hybrid set is defined as the combination of set R = {x, y} and set S = {y, z}, which of the following is the correct representation of the hybrid set?
A.
{x, y, z}
B.
{y}
C.
{x, y}
D.
{y, z}
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Solution
The hybrid set formed by combining set R and set S includes all unique elements from both sets, which are {x, y, z}.
Correct Answer:
A
— {x, y, z}
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Q. If a hybrid set is defined as the combination of two sets with some overlapping elements, which of the following is a characteristic of such a set?
A.
It cannot contain duplicate elements.
B.
It must contain all elements from both sets.
C.
It can only contain elements from one of the sets.
D.
It is always larger than the individual sets.
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Solution
A hybrid set cannot contain duplicate elements, as it is defined to include unique elements from both sets.
Correct Answer:
A
— It cannot contain duplicate elements.
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Q. If a hybrid set is defined as the intersection of two sets, which of the following is true?
A.
It contains all elements from both sets.
B.
It contains only the elements that are common to both sets.
C.
It can be empty if there are no common elements.
D.
Both B and C are correct.
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Solution
The intersection of two sets contains only the elements that are common to both sets, and it can be empty if there are no common elements.
Correct Answer:
D
— Both B and C are correct.
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Q. If a hybrid set is defined as the union of sets A = {a, b} and B = {b, c}, what is the resulting hybrid set? (2023)
A.
{a, b, c}
B.
{b}
C.
{a, b, b, c}
D.
{a, c}
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Solution
The union of sets A and B combines all unique elements, resulting in the hybrid set {a, b, c}.
Correct Answer:
A
— {a, b, c}
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Q. If a set A contains elements {1, 2, 3, 4, 5} and a constraint states that only even numbers can be included, what will be the resulting set?
A.
{2, 4}
B.
{1, 3, 5}
C.
{1, 2, 3, 4, 5}
D.
{}
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Solution
The resulting set will be {2, 4} as these are the only even numbers in set A.
Correct Answer:
A
— {2, 4}
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Q. If a set A is defined by the constraints x > 5 and x < 10, which of the following numbers is NOT a member of set A?
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Solution
The number 10 does not satisfy the constraint x < 10, hence it is not a member of set A.
Correct Answer:
C
— 10
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Q. If a set D is defined as {x | x is a positive integer and x is less than or equal to 15}, how many elements are in set D?
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Solution
Set D includes all positive integers from 1 to 15, which totals 15 elements.
Correct Answer:
B
— 15
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Q. If a set is defined as containing all prime numbers less than 20, which of the following numbers is NOT 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 fruit and x is red}, which of the following fruits would NOT be included in this set?
A.
Apple
B.
Banana
C.
Cherry
D.
Strawberry
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Solution
The fruit 'Banana' would not be included in the set as it is not red.
Correct Answer:
B
— Banana
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Q. If a set is defined as {x | x is a letter in the English alphabet and x is a consonant}, which of the following letters is NOT included in this set?
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Solution
The letter E is a vowel and therefore not included in the set of consonants.
Correct Answer:
B
— E
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Q. If a set is defined as {x | x is a letter in the English alphabet and x is a vowel}, which of the following is an element of this set?
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Solution
The letter A is an element of the set as it is a vowel in the English alphabet.
Correct Answer:
C
— A
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Q. If a set is defined as {x | x is a letter in the English alphabet and x is a vowel}, which of the following letters is NOT an element of this set?
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Solution
The letter Z is not a vowel and therefore is not an element of the set defined by vowels.
Correct Answer:
D
— Z
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Q. If a set is defined as {x | x is a letter in the English alphabet that is a vowel}, which of the following letters is NOT in the set?
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Solution
The vowels in the English alphabet are A, E, I, O, and U. The letter Y is sometimes considered a vowel but is not classified as one in this context.
Correct Answer:
D
— Y
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Q. If a set is defined as {x | x is a natural number and x < 10}, which of the following is the largest element in this set?
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Solution
The largest natural number less than 10 is 9, making it the largest element in the defined set.
Correct Answer:
B
— 9
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Q. If a set is defined as {x | x is a natural number and x < 10}, which of the following is a valid element of this set?
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Solution
The valid element of the set is 5, as it is a natural number and less than 10.
Correct Answer:
B
— 5
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Q. If a set is defined as {x | x is a natural number and x < 10}, which of the following is the correct representation of this set?
A.
{1, 2, 3, 4, 5, 6, 7, 8, 9}
B.
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
C.
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
D.
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
Show solution
Solution
The correct representation of the set is {1, 2, 3, 4, 5, 6, 7, 8, 9}, as it includes all natural numbers less than 10.
Correct Answer:
A
— {1, 2, 3, 4, 5, 6, 7, 8, 9}
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Q. If a set is defined as {x | x is a natural number and x < 5}, which of the following elements is NOT part of this set?
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Solution
The element '5' is not part of the set because the constraint specifies that x must be less than 5.
Correct Answer:
C
— 5
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Q. If a set is defined as {x | x is a natural number less than 20 and even}, which of the following numbers is included in the set?
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Solution
The even natural numbers less than 20 are 2, 4, 6, 8, 10, 12, 14, 16, and 18. Therefore, 10 is included in the set.
Correct Answer:
C
— 10
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Q. If a set is defined as {x | x is a positive integer and x is a divisor of 12}, which of the following is NOT an element of this set?
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Solution
The divisors of 12 are 1, 2, 3, 4, and 6, so 5 is not an element of this set.
Correct Answer:
D
— 5
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