Q. A group of friends consists of 10 people. If 6 like football, 4 like basketball, and 2 like both, how many like neither sport?
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Solution
Using the inclusion-exclusion principle: Total liking at least one sport = 6 + 4 - 2 = 8. Therefore, those liking neither = 10 - 8 = 2.
Correct Answer:
C
— 6
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Q. A group of friends consists of 12 people who like either football or basketball. If 7 like football and 5 like basketball, how many like both?
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Solution
Using the principle of inclusion-exclusion: Total = Football + Basketball - Both. Thus, 12 = 7 + 5 - Both, leading to Both = 0.
Correct Answer:
B
— 2
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Q. A group of friends consists of 12 people who like either football or basketball. If 7 like football and 5 like both, how many like only basketball?
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Solution
Let B be the number of basketball players. Total = Football + Basketball - Both. 12 = 7 + B - 5. Thus, B = 10, and only basketball = 10 - 5 = 5.
Correct Answer:
B
— 2
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Q. A group of friends consists of 12 people 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 people who play only football, we subtract those who play both from those who play football: 12 - 5 = 7.
Correct Answer:
A
— 7
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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?
Show solution
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 people who like football, 3 who like basketball, and 2 who like both. How many like only football? (2023)
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Solution
To find the number of friends who like only football, we subtract those who like both from those who like football: 5 - 2 = 3.
Correct Answer:
A
— 3
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Q. A group of friends consists of 5 people who play football, 4 who play basketball, and 2 who play both. How many friends play only one sport?
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Solution
To find the number of friends who play only one sport, we calculate: (Football only + Basketball only) = (5 - 2) + (4 - 2) = 3 + 2 = 5.
Correct Answer:
B
— 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 = {1, 2, 3, 4} and set B = {3, 4, 5, 6}, what is the difference A - B?
A.
{1, 2}
B.
{3, 4}
C.
{5, 6}
D.
{}
Show solution
Solution
The difference A - B includes elements in A that are not in B, which are {1, 2}.
Correct Answer:
A
— {1, 2}
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Q. If set A = {1, 2, 3, 4} and set B = {3, 4, 5, 6}, what is the intersection of sets A and B? (2023)
A.
{1, 2}
B.
{3, 4}
C.
{5, 6}
D.
{1, 2, 5, 6}
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Solution
The intersection of sets A and B includes the 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 = {1, 2, 3} and set B = {2, 3, 4}, what is A - B? (2023)
A.
{1}
B.
{2, 3}
C.
{3, 4}
D.
{}
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Solution
A - B represents the elements in A that are not in B. Thus, A - B = {1}.
Correct Answer:
A
— {1}
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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}
Show solution
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}
Show solution
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 C = {x | x is a multiple of 3 and less than 30}, how many elements are in set C?
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Solution
The multiples of 3 less than 30 are {3, 6, 9, 12, 15, 18, 21, 24, 27}, totaling 9 elements.
Correct Answer:
B
— 9
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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}
Show solution
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 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}
Show solution
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 P ∩ Q?
A.
{2, 4, 6, 8}
B.
{2, 3, 5, 7}
C.
{2}
D.
{4, 6, 8}
Show solution
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 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}
Show solution
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 the intersection of sets P and Q?
A.
{2, 4, 6, 8}
B.
{2, 3, 5, 7}
C.
{2}
D.
{4, 6, 8}
Show solution
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}
Show solution
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.
{}
Show solution
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}
Show solution
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 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}
Show solution
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, 7, 8, 9, 10}, set A = {2, 4, 6, 8}, and set B = {1, 2, 3}, what is the complement of A?
A.
{1, 3, 5, 7, 9, 10}
B.
{1, 3, 5, 7, 9}
C.
{2, 4, 6, 8}
D.
{1, 2, 3}
Show solution
Solution
The complement of A in U is the set of elements in U that are not in A, which is {1, 3, 5, 7, 9, 10}.
Correct Answer:
A
— {1, 3, 5, 7, 9, 10}
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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}
Show solution
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. If the universal set U has 100 elements, set A has 40 elements, and set B has 30 elements with 10 elements in both A and B, how many elements are in neither A nor B?
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Solution
Using the principle of inclusion-exclusion, the number of elements in either A or B is: (A + B - Both) = 40 + 30 - 10 = 60. Therefore, elements in neither = U - (A ∪ B) = 100 - 60 = 40.
Correct Answer:
A
— 60
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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 40 students, 25 study English, 15 study Mathematics, and 10 study both. How many students study only English?
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Solution
Students who study only English = Total English - Both = 25 - 10 = 15.
Correct Answer:
A
— 15
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Q. In a class of 40 students, 25 study English, 20 study Mathematics, and 10 study both. How many study only Mathematics?
Show solution
Solution
To find the number of students who study only Mathematics, we subtract those who study both from those who study Mathematics: 20 - 10 = 10.
Correct Answer:
B
— 15
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Showing 1 to 30 of 50 (2 Pages)
Set Theory MCQ & Objective Questions
Set Theory is a fundamental concept in mathematics that plays a crucial role in various exams. Understanding this topic is essential for students aiming to excel in their school exams and competitive tests. Practicing Set Theory MCQs and objective questions not only enhances conceptual clarity but also boosts your confidence in tackling important questions during exams.
What You Will Practise Here
Basic definitions and notation of sets
Types of sets: finite, infinite, equal, and null sets
Set operations: union, intersection, and difference
Venn diagrams and their applications
Power sets and Cartesian products
Applications of set theory in real-life scenarios
Important formulas and theorems related to sets
Exam Relevance
Set Theory is a significant topic in various educational boards, including CBSE and State Boards. It frequently appears in the form of MCQs, short answer questions, and problem-solving questions in exams like NEET and JEE. Students can expect questions that test their understanding of set operations, Venn diagrams, and the application of set theory in problem-solving. Familiarity with common question patterns will aid in better preparation and scoring.
Common Mistakes Students Make
Confusing the concepts of union and intersection
Misinterpreting Venn diagrams and their representations
Overlooking the importance of null sets and their properties
Struggling with the application of set operations in word problems
FAQs
Question: What are the basic operations in Set Theory?Answer: The basic operations in Set Theory include union, intersection, and difference of sets.
Question: How can Venn diagrams help in understanding Set Theory?Answer: Venn diagrams visually represent the relationships between sets, making it easier to understand operations like union and intersection.
Now is the time to enhance your understanding of Set Theory! Dive into our practice MCQs and test your knowledge on important Set Theory questions for exams. The more you practice, the better you will score!
