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 P = {1, 2, 3, 4} and set Q = {3, 4, 5, 6}, what is the difference P - Q?
-
A.
{1, 2}
-
B.
{3, 4}
-
C.
{5, 6}
-
D.
{1, 2, 5, 6}
Solution
The difference P - Q includes elements in P that are not in Q, which is {1, 2}.
Correct Answer:
A
— {1, 2}
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Q. If set P = {x | x is an even number less than 10} and set Q = {x | x is a prime number less than 10}, what is the intersection of sets P and Q?
-
A.
{2, 4, 6, 8}
-
B.
{2, 3, 5, 7}
-
C.
{2}
-
D.
{4, 6, 8}
Solution
The intersection of sets P and Q includes elements that are both even and prime. The only even prime number is 2.
Correct Answer:
C
— {2}
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Q. If set P = {x | x is an even number less than 10} and set Q = {x | x is a prime number less than 10}, what is the union of sets P and Q?
-
A.
{2, 3, 4, 5, 6, 8}
-
B.
{2, 3, 5, 7}
-
C.
{2, 4, 6, 8}
-
D.
{2, 3, 4, 5, 7, 8}
Solution
Set P = {2, 4, 6, 8} and set Q = {2, 3, 5, 7}. The union is {2, 3, 4, 5, 6, 7, 8}.
Correct Answer:
D
— {2, 3, 4, 5, 7, 8}
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Q. If set P = {x | x is an even number less than 10} and set Q = {x | x is a prime number less than 10}, what is the difference P - Q?
-
A.
{2, 4, 6, 8}
-
B.
{4, 6, 8}
-
C.
{2, 6, 8}
-
D.
{2, 4, 6, 8, 3, 5, 7}
Solution
Set P = {2, 4, 6, 8} and set Q = {2, 3, 5, 7}. The difference P - Q = {4, 6, 8}.
Correct Answer:
B
— {4, 6, 8}
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Q. If set P = {x | x is an even number less than 10} and set Q = {x | x is a prime number less than 10}, what is P ∩ Q?
-
A.
{2, 4, 6, 8}
-
B.
{2, 3, 5, 7}
-
C.
{2}
-
D.
{4, 6, 8}
Solution
The intersection P ∩ Q includes only the even prime number, which is {2}.
Correct Answer:
C
— {2}
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Q. If set R = {1, 2, 3, 4, 5} and set S = {4, 5, 6, 7}, what is the symmetric difference of sets R and S?
-
A.
{1, 2, 3, 6, 7}
-
B.
{4, 5}
-
C.
{1, 2, 3, 4, 5, 6, 7}
-
D.
{6, 7}
Solution
The symmetric difference of sets R and S includes elements that are in either set but not in both. Thus, it is {1, 2, 3, 6, 7}.
Correct Answer:
A
— {1, 2, 3, 6, 7}
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Q. If set R = {1, 2, 3, 4} and set S = {3, 4, 5, 6}, what is the difference R - S?
-
A.
{1, 2}
-
B.
{3, 4}
-
C.
{5, 6}
-
D.
{}
Solution
The difference R - S includes elements in R that are not in S, which is {1, 2}.
Correct Answer:
A
— {1, 2}
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Q. If set R = {1, 2, 3, 4} and set S = {3, 4, 5, 6}, what is the symmetric difference of sets R and S?
-
A.
{1, 2, 5, 6}
-
B.
{3, 4}
-
C.
{1, 2, 3, 4, 5, 6}
-
D.
{3, 4, 5}
Solution
The symmetric difference is the set of elements in either set R or set S but not in both, which is {1, 2, 5, 6}.
Correct Answer:
A
— {1, 2, 5, 6}
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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 = {a, b, c} and set Y = {b, c, d}, what is the union of sets X and Y?
-
A.
{a, b, c, d}
-
B.
{b, c}
-
C.
{a, b}
-
D.
{c, d}
Solution
The union of sets X and Y includes all unique elements from both sets. Thus, the union is {a, b, c, d}.
Correct Answer:
A
— {a, b, c, d}
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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 sin 2A = 2 sin A cos A, what is the double angle formula for cosine?
-
A.
cos 2A = cos²A - sin²A
-
B.
cos 2A = 2 sin A cos A
-
C.
cos 2A = sin²A - cos²A
-
D.
cos 2A = 1 - 2 sin²A
Solution
The double angle formula for cosine is cos 2A = cos²A - sin²A.
Correct Answer:
A
— cos 2A = cos²A - sin²A
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Q. If sin 2A = 2 sin A cos A, what is the value of sin 2A when sin A = 1/2?
Solution
Using the double angle formula, sin 2A = 2(1/2)(√(1 - (1/2)²)) = 2(1/2)(√(3/4)) = 1.
Correct Answer:
B
— 1
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Q. If sin 2θ = 2 sin θ cos θ, what is the value of sin 2(30°)?
Solution
sin 2(30°) = sin 60° = √3/2.
Correct Answer:
C
— √3/2
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Q. If sin A = 0, what is the value of A? (2019)
-
A.
0°
-
B.
90°
-
C.
180°
-
D.
360°
Solution
Sin A = 0 at A = 0°, 180°, and 360°. The principal value is 0°.
Correct Answer:
A
— 0°
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Q. If sin A = 0.6, what is cos A?
-
A.
0.8
-
B.
0.6
-
C.
0.4
-
D.
0.2
Solution
Using the identity sin^2 A + cos^2 A = 1, we have cos A = sqrt(1 - (0.6)^2) = sqrt(1 - 0.36) = sqrt(0.64) = 0.8.
Correct Answer:
A
— 0.8
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Q. If sin A = 0.6, what is the value of cos A to two decimal places?
-
A.
0.8
-
B.
0.6
-
C.
0.4
-
D.
0.2
Solution
Using the Pythagorean identity, cos A = √(1 - sin²A) = √(1 - 0.36) = √(0.64) = 0.8.
Correct Answer:
A
— 0.8
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