Q. How many subsets can be formed from the set S = {a, b, c, d}?
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Solution
The number of subsets of a set with n elements is 2^n. Here, n = 4, so the number of subsets is 2^4 = 16.
Correct Answer:
B
— 8
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Q. How many subsets does the set A = {a, b, c} have?
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Solution
The number of subsets of a set with n elements is 2^n. Here, n = 3, so the number of subsets is 2^3 = 8.
Correct Answer:
D
— 8
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Q. How many subsets does the set {a, b, c} have?
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Solution
The number of subsets of a set with n elements is 2^n. Here, n = 3, so the number of subsets is 2^3 = 8.
Correct Answer:
D
— 8
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Q. If A = {1, 2, 3, 4} and B = {2, 4, 6, 8}, what is A ∪ B?
A.
{1, 2, 3, 4, 6, 8}
B.
{2, 4}
C.
{1, 3, 5, 7}
D.
{1, 2, 3, 4, 5}
Show solution
Solution
The union A ∪ B includes all elements from both sets, which are {1, 2, 3, 4, 6, 8}.
Correct Answer:
A
— {1, 2, 3, 4, 6, 8}
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Q. If A = {1, 2, 3} and B = {1, 2, 3, 4, 5}, what is A ⊆ B?
A.
True
B.
False
C.
Depends on the context
D.
None of the above
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Solution
Set A is a subset of set B because all elements of A are contained in B. Therefore, A ⊆ B is True.
Correct Answer:
A
— True
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Q. If A = {1, 2, 3} and B = {1, 2, 3, 4}, what is the cardinality of A × B?
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Solution
The cardinality of the Cartesian product A × B is given by |A| * |B|. Here, |A| = 3 and |B| = 4, so |A × B| = 3 * 4 = 12.
Correct Answer:
B
— 6
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Q. If A = {1, 2, 3} and B = {1, 2, 3}, what is A × B?
A.
{(1,1), (2,2), (3,3)}
B.
{(1,2), (2,3), (3,1)}
C.
{(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}
D.
{}
Show solution
Solution
A × B = {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)} as it is the Cartesian product of A and B.
Correct Answer:
C
— {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}
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Q. If A = {1, 2, 3} and B = {3, 4, 5}, what is A - B?
A.
{1, 2}
B.
{3}
C.
{4, 5}
D.
{1, 2, 3, 4, 5}
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Solution
The difference of sets A and B, A - B, contains elements that are in A but not in B. Here, A - B = {1, 2}.
Correct Answer:
A
— {1, 2}
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Q. If A = {1, 2, 3} and B = {3, 4, 5}, what is A Δ B (symmetric difference)?
A.
{1, 2}
B.
{4, 5}
C.
{1, 2, 4, 5}
D.
{3}
Show solution
Solution
The symmetric difference A Δ B includes elements in either A or B but not in both, which are {1, 2, 4, 5}.
Correct Answer:
C
— {1, 2, 4, 5}
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Q. If A = {1, 2, 3} and B = {3, 4, 5}, what is A ∪ (A ∩ B)?
A.
{1, 2, 3}
B.
{3, 4, 5}
C.
{1, 2, 3, 4, 5}
D.
{1, 2, 5}
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Solution
First, A ∩ B = {3}. Then, A ∪ {3} = {1, 2, 3}.
Correct Answer:
A
— {1, 2, 3}
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Q. If A = {x | x is a letter in the word 'MATH'} and B = {x | x is a letter in the word 'SET'}, what is A ∩ B?
A.
{M, A, T}
B.
{A, T}
C.
{T}
D.
{}
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Solution
The intersection A ∩ B consists of common letters, which is {T}.
Correct Answer:
C
— {T}
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Q. If A = {x | x is a letter in the word 'MATH'} and B = {x | x is a letter in the word 'SCIENCE'}, what is A ∩ B?
A.
{A}
B.
{M, A, T}
C.
{A, C, E}
D.
{A, T}
Show solution
Solution
The intersection A ∩ B includes letters that are common in both words. The only common letter is 'A', so A ∩ B = {A}.
Correct Answer:
A
— {A}
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Q. If A = {x | x is a multiple of 3} and B = {x | x is a multiple of 5}, what is A ∩ B?
A.
{15}
B.
{3, 5}
C.
{0}
D.
{}
Show solution
Solution
The intersection A ∩ B consists of common multiples, which is {0}.
Correct Answer:
C
— {0}
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Q. If A = {x | x is a natural number and x < 5} and B = {x | x is a natural number and x > 2}, what is A ∩ B?
A.
{1, 2}
B.
{3, 4}
C.
{2, 3, 4}
D.
{1, 2, 3, 4}
Show solution
Solution
Set A = {1, 2, 3, 4} and set B = {3, 4, 5, ...}. The intersection A ∩ B = {3, 4}.
Correct Answer:
B
— {3, 4}
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Q. If A = {x | x is a natural number less than 5} and B = {x | x is a natural number less than 3}, what is A - B?
A.
{1, 2}
B.
{3, 4}
C.
{1, 2, 3, 4}
D.
{2, 3, 4}
Show solution
Solution
Set A = {1, 2, 3, 4} and set B = {1, 2}. Thus, A - B = {3, 4}.
Correct Answer:
B
— {3, 4}
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Q. If A = {x | x is a natural number less than 5} and B = {x | x is an odd natural number}, what is A ∩ B?
A.
{1, 2, 3, 4}
B.
{1, 3}
C.
{2, 4}
D.
{1, 2, 3}
Show solution
Solution
The intersection A ∩ B includes elements that are in both A and B. Here, A = {1, 2, 3, 4} and B = {1, 3}, so A ∩ B = {1, 3}.
Correct Answer:
B
— {1, 3}
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Q. If A = {x | x is a prime number less than 10} and B = {2, 3, 5, 7}, what is A = B?
A.
True
B.
False
C.
Cannot be determined
D.
None of the above
Show solution
Solution
Both sets A and B contain the same elements: {2, 3, 5, 7}. Therefore, A = B is True.
Correct Answer:
A
— True
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Q. If A = {x | x is a prime number less than 10} and B = {2, 3, 5, 7}, what is A?
A.
{2, 3, 5, 7}
B.
{1, 2, 3, 4, 5, 6, 7, 8, 9}
C.
{2, 3, 5, 7, 11}
D.
{2, 3, 5, 7, 9}
Show solution
Solution
The set A consists of all prime numbers less than 10, which are {2, 3, 5, 7}.
Correct Answer:
A
— {2, 3, 5, 7}
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Q. If A = {x | x is a vowel} and B = {x | x is a consonant}, what is A ∩ B?
A.
{a, e, i, o, u}
B.
{}
C.
{a, b, c}
D.
{a, e, i}
Show solution
Solution
The intersection A ∩ B is empty because no letter can be both a vowel and a consonant.
Correct Answer:
B
— {}
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Q. If A = {x | x is an even integer} and B = {x | x is a multiple of 3}, what is A ∪ B?
A.
{0, 2, 4, 6, ...}
B.
{0, 3, 6, 9, ...}
C.
{0, 2, 3, 4, 6, 9, ...}
D.
{0, 2, 3, 4, 6, 8, 9, ...}
Show solution
Solution
The union of sets A and B, A ∪ B, includes all even integers and all multiples of 3. Thus, A ∪ B = {0, 2, 3, 4, 6, 9, ...}.
Correct Answer:
C
— {0, 2, 3, 4, 6, 9, ...}
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Q. If A = {x | x is an even integer} and B = {x | x is a prime number}, what is A ∩ B?
A.
{2}
B.
{2, 3}
C.
{2, 4}
D.
{}
Show solution
Solution
The only even prime number is 2, so A ∩ B = {2}.
Correct Answer:
A
— {2}
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Q. If A = {x | x is an even number} and B = {x | x is a prime number}, what is A ∩ B?
A.
{2}
B.
{2, 3}
C.
{2, 4}
D.
{}
Show solution
Solution
A ∩ B = {2} as 2 is the only even prime number.
Correct Answer:
A
— {2}
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Q. If R is a relation on set A = {1, 2, 3} defined by R = {(1, 1), (2, 2), (3, 3)}, is R symmetric?
A.
Yes
B.
No
C.
Depends on A
D.
None of the above
Show solution
Solution
A relation is symmetric if for every (a, b) in R, (b, a) is also in R. Since R only contains pairs of the form (a, a), it is symmetric.
Correct Answer:
A
— Yes
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Q. If the relation R on set A = {1, 2, 3} is defined as R = {(1, 2), (2, 3)}, is R reflexive?
A.
Yes
B.
No
C.
Depends on A
D.
None of the above
Show solution
Solution
A relation is reflexive if every element is related to itself. Here, (1,1), (2,2), and (3,3) are not in R, so R is not reflexive.
Correct Answer:
B
— No
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Q. If the universal set U = {1, 2, 3, 4, 5} and A = {1, 2}, what is A'?
A.
{3, 4, 5}
B.
{1, 2}
C.
{1, 2, 3}
D.
{2, 3, 4, 5}
Show solution
Solution
The complement of A, denoted A', includes all elements in U that are not in A. Thus, A' = {3, 4, 5}.
Correct Answer:
A
— {3, 4, 5}
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Q. If U = {1, 2, 3, 4, 5}, A = {1, 2}, and B = {2, 3}, what is A ∪ B?
A.
{1, 2}
B.
{1, 2, 3}
C.
{1, 2, 3, 4, 5}
D.
{2, 3, 4, 5}
Show solution
Solution
The union A ∪ B includes all elements from both sets, which are {1, 2, 3}.
Correct Answer:
B
— {1, 2, 3}
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Showing 1 to 26 of 26 (1 Pages)
Sets & Relations MCQ & Objective Questions
Understanding "Sets & Relations" is crucial for students preparing for various exams in India. This topic forms the backbone of many mathematical concepts and is frequently tested in school and competitive exams. Practicing MCQs and objective questions on Sets & Relations not only enhances conceptual clarity but also boosts your confidence, helping you score better in your exams.
What You Will Practise Here
Fundamentals of Sets: Definitions and Notations
Types of Sets: Finite, Infinite, Equal, and Null Sets
Operations on Sets: Union, Intersection, and Complement
Relations: Definition, Types, and Properties
Functions: One-to-One, Onto, and Inverse Functions
Venn Diagrams: Visual Representation of Sets
Important Formulas and Theorems related to Sets and Relations
Exam Relevance
The topic of Sets & Relations is a significant part of the syllabus for CBSE, State Boards, and competitive exams like NEET and JEE. Students can expect questions that require them to apply concepts in various contexts, such as solving problems involving Venn diagrams or identifying properties of relations. Common question patterns include multiple-choice questions that test both theoretical understanding and practical application of the concepts.
Common Mistakes Students Make
Confusing different types of sets and their properties.
Misunderstanding the operations on sets, especially union and intersection.
Overlooking the importance of notation and definitions in problems.
Failing to accurately interpret Venn diagrams in relation to set operations.
Neglecting to check whether a function is one-to-one or onto.
FAQs
Question: What are the key concepts I should focus on in Sets & Relations?Answer: Focus on understanding types of sets, operations on sets, and properties of relations and functions.
Question: How can I improve my performance in Sets & Relations MCQs?Answer: Regular practice of objective questions and reviewing common mistakes will significantly enhance your understanding and performance.
Now is the time to sharpen your skills! Dive into our practice MCQs on Sets & Relations and test your understanding to excel in your exams.
