Q. A group of friends consists of 12 who play football, 8 who play basketball, and 5 who play both. How many play only football?
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Solution
To find the number of friends who play only football, we subtract those who play both from those who play football: 12 - 5 = 7.
Correct Answer: C — 7
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Q. A group of friends consists of 5 who like football, 4 who like basketball, and 2 who like both. How many friends like only football?
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Solution
The number of friends who like only football is calculated as: Only Football = Total Football - Both = 5 - 2 = 3.
Correct Answer: A — 3
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Q. If set A = {x | x is an even number less than 10} and set B = {x | x is a prime number less than 10}, what is A ∩ B?
A.
{2, 4, 6, 8}
B.
{2}
C.
{2, 3, 5, 7}
D.
{2, 3, 5, 7, 4, 6, 8}
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Solution
The intersection A ∩ B includes elements that are both even and prime, which is {2}.
Correct Answer: B — {2}
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Q. If set A contains the elements {1, 2, 3, 4} and set B contains the elements {3, 4, 5, 6}, what is the intersection of sets A and B?
A.
{1, 2}
B.
{3, 4}
C.
{5, 6}
D.
{1, 2, 3, 4, 5, 6}
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Solution
The intersection of sets A and B is the set of elements that are common to both sets. Therefore, the intersection is {3, 4}.
Correct Answer: B — {3, 4}
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Q. If set A contains the numbers {1, 2, 3, 4, 5} and set B contains the numbers {4, 5, 6, 7, 8}, what is the intersection of sets A and B?
A.
{1, 2, 3}
B.
{4, 5}
C.
{6, 7, 8}
D.
{1, 2, 3, 4, 5, 6, 7, 8}
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Solution
The intersection of sets A and B is the set of elements that are common to both sets, which is {4, 5}.
Correct Answer: B — {4, 5}
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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}
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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}
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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 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}
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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 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}
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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 the universal set U = {1, 2, 3, 4, 5, 6} and set A = {2, 4, 6}, what is the complement of set A?
A.
{1, 2, 3}
B.
{1, 3, 5}
C.
{2, 4, 6}
D.
{4, 5, 6}
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Solution
The complement of set A consists of elements in the universal set U that are not in set A. Therefore, the complement is {1, 3, 5}.
Correct Answer: B — {1, 3, 5}
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Q. In a class of 30 students, 18 students study Mathematics, 15 study Science, and 10 study both subjects. How many students study only Mathematics?
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Solution
To find the number of students who study only Mathematics, we use the formula: Only Mathematics = Total Mathematics - Both subjects. Thus, 18 - 10 = 8.
Correct Answer: A — 8
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Q. In a class of 50 students, 20 study English, 25 study Hindi, and 10 study both. How many students study only Hindi?
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Solution
To find the number of students who study only Hindi, we subtract those who study both from those who study Hindi: 25 - 10 = 15.
Correct Answer: A — 15
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Q. In a class, 12 students play cricket, 15 play football, and 5 play both. How many students play either cricket or football?
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Solution
Using inclusion-exclusion, the number of students who play either sport is: (Cricket + Football - Both) = 12 + 15 - 5 = 22.
Correct Answer: A — 22
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Q. In a survey of 100 people, 60 like chocolate, 50 like vanilla, and 20 like both. How many like only chocolate?
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Solution
To find the number of people who like only chocolate, we subtract those who like both from those who like chocolate: 60 - 20 = 40.
Correct Answer: A — 30
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Q. In a survey, 40 people like tea, 30 like coffee, and 10 like both. How many people like either tea or coffee?
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Solution
Using the principle of inclusion-exclusion, the number of people who like either tea or coffee is: (Tea + Coffee - Both) = 40 + 30 - 10 = 60.
Correct Answer: A — 60
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Q. In a survey, 40 people like tea, 30 like coffee, and 10 like both. How many people like only tea?
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Solution
To find the number of people who like only tea, we subtract those who like both from those who like tea: 40 - 10 = 30.
Correct Answer: B — 20
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Q. In a survey, 50 people like apples, 40 like bananas, and 20 like both. How many people like only bananas?
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Solution
The number of people who like only bananas is calculated as: Only Bananas = Total Bananas - Both = 40 - 20 = 20.
Correct Answer: B — 30
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