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By rohit.pandey1
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Updated on 9 Jun 2026, 12:55 IST
Sets is the first chapter of Class 11 Maths and forms the foundation for important topics such as Relations and Functions, Probability, Mathematical Reasoning, and advanced mathematics. A strong understanding of sets is essential for solving questions involving Venn diagrams, subsets, power sets, union, intersection, complement of sets, and De Morgan's Laws.
To help students revise the chapter effectively, we have compiled 80+ Sets MCQ Questions with Answers covering all important concepts from the latest NCERT and CBSE syllabus. These CBSE Class 11 Maths MCQs include basic concept-based MCQs, application-oriented questions, assertion-reason questions, case study-based MCQs, and Venn diagram problems along with detailed solutions and explanations.
Whether you are preparing for Class 11 school exams, CBSE assessments, Olympiads, scholarship exams, or IIT JEE Foundation, these Sets MCQ Questions will help you strengthen your concepts, improve accuracy, and gain confidence in solving objective-type mathematics questions.
A set is a well-defined collection of objects. The objects in a set are called elements or members of the set.
For example:
{a, e, i, o, u}{1, 2, 3, 4}In sets, elements are usually written inside curly brackets { }.
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| Symbol | Meaning | Example |
| ∈ | belongs to | 2 ∈ {1, 2, 3} |
| ∉ | does not belong to | 5 ∉ {1, 2, 3} |
| ∅ | empty set | A = ∅ |
| ⊆ | subset | A ⊆ B |
| ⊂ | proper subset | A ⊂ B |
| ∪ | union | A ∪ B |
| ∩ | intersection | A ∩ B |
| A' | complement of A | A' = U − A |
| A − B | difference of sets | Elements in A but not in B |
| P(A) | power set of A | Set of all subsets of A |
| Concept | Formula |
| Number of subsets of A | If n(A) = m, then number of subsets = 2^m |
| Number of proper subsets of A | 2^m − 1 |
| Number of elements in power set | n(P(A)) = 2^m |
| Union of two sets | n(A ∪ B) = n(A) + n(B) − n(A ∩ B) |
| Number of elements in only A | n(A only) = n(A) − n(A ∩ B) |
| Number of elements in only B | n(B only) = n(B) − n(A ∩ B) |
| Union of three sets | n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A ∩ B) − n(B ∩ C) − n(C ∩ A) + n(A ∩ B ∩ C) |
| De Morgan’s first law | (A ∪ B)' = A' ∩ B' |
| De Morgan’s second law | (A ∩ B)' = A' ∪ B' |
(a) Collection of good students
(b) Collection of beautiful paintings
(c) Collection of vowels in the English alphabet
(d) Collection of difficult questions
Answer: (c) Collection of vowels in the English alphabet
Explanation: A set must be well-defined. The vowels in the English alphabet are fixed: {a, e, i, o, u}. Words like good, beautiful, and difficult are subjective.
(a) 3 ∈ A
(b) 4 ∈ A
(c) 5 ∈ A
(d) 10 ∈ A
Answer: (b) 4 ∈ A
Explanation: The symbol ∈ means “belongs to”. Since 4 is an element of A, we write 4 ∈ A.
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(a) An element of A
(b) A subset of A
(c) Not an element of A
(d) Equal to A
Answer: (c) Not an element of A
Explanation: The set A contains only 1, 3, 5, and 7. Therefore, 2 ∉ A.
(a) {0, 1, 2, 3, 4, 5}
(b) {1, 2, 3, 4, 5}
(c) {1, 2, 3, 4, 5, 6}
(d) {2, 3, 4, 5, 6}
Answer: (b) {1, 2, 3, 4, 5}
Explanation: Natural numbers start from 1. Natural numbers less than 6 are 1, 2, 3, 4, and 5.
(a) {M, A, T, H, S}
(b) {M, A, T, H}
(c) {MATHS}
(d) {A, T, H, S}
Answer: (a) {M, A, T, H, S}
Explanation: Each letter of the word is written as an element of the set.
(a) {0}
(b) {∅}
(c) {x : x is a natural number less than 1}
(d) {1}
Answer: (c) {x : x is a natural number less than 1}
Explanation: There is no natural number less than 1. Hence, the set has no element and is an empty set.
(a) Collection of prime numbers less than 10
(b) Collection of months in a year
(c) Collection of tall boys in a class
(d) Collection of even numbers less than 20
Answer: (c) Collection of tall boys in a class
Explanation: The word “tall” is not clearly defined. Different people may have different opinions, so it is not a well-defined collection.
(a) 4
(b) 5
(c) 6
(d) 10
Answer: (b) 5
Explanation: The number of elements in a set is called its cardinal number. Here, A has 5 elements.
(a) {1, 2, 3, 4, 5}
(b) {2, 4, 6, 8}
(c) {0, 2, 4, 6, 8}
(d) {2, 4, 6, 8, 10}
Answer: (b) {2, 4, 6, 8}
Explanation: Even natural numbers less than 10 are 2, 4, 6, and 8.
(a) {1, 2, 3, 5, 7, 11, 13}
(b) {2, 3, 5, 7, 11, 13}
(c) {2, 4, 6, 8, 10, 12, 14}
(d) {3, 5, 7, 9, 11, 13}
Answer: (b) {2, 3, 5, 7, 11, 13}
Explanation: Prime numbers have exactly two factors: 1 and the number itself. 1 is not a prime number.
(a) {x : x is a natural number less than 6}
(b) {x : x is an even number less than 6}
(c) {x : x is a prime number less than 6}
(d) {x : x is an integer greater than 6}
Answer: (a) {x : x is a natural number less than 6}
Explanation: The elements 1, 2, 3, 4, and 5 are natural numbers less than 6.
(a) {S, C, H, O, O, L}
(b) {S, C, H, O, L}
(c) {SCHOOL}
(d) {S, C, H, L}
Answer: (b) {S, C, H, O, L}
Explanation: Repeated elements are written only once in a set. The letter O appears twice in the word, but it is listed once in the set.
(a) {1, 2, 3, 4, 6, 12}
(b) {2, 3, 4, 6}
(c) {1, 2, 6, 12}
(d) {1, 3, 6, 12}
Answer: (a) {1, 2, 3, 4, 6, 12}
Explanation: The factors of 12 are 1, 2, 3, 4, 6, and 12.
(a) {1, 2, 3}
(b) {0, 1, 2, 3}
(c) {0, 1, 2, 3, 4}
(d) {2, 3, 4}
Answer: (b) {0, 1, 2, 3}
Explanation: Whole numbers start from 0. Whole numbers less than 4 are 0, 1, 2, and 3.
(a) {x : x is an odd natural number less than 12}
(b) {x : x is an even natural number less than or equal to 10}
(c) {x : x is a prime number less than 10}
(d) {x : x is a factor of 10}
Answer: (b) {x : x is an even natural number less than or equal to 10}
Explanation: The elements are even natural numbers from 2 to 10.
(a) {A, P, P, L, E}
(b) {A, P, L, E}
(c) {APPLE}
(d) {A, L, E}
Answer: (b) {A, P, L, E}
Explanation: In a set, repeated elements are not written more than once.
(a) Singleton set
(b) Universal set
(c) Empty set
(d) Power set
Answer: (c) Empty set
Explanation: A set with no element is called an empty set or null set. It is denoted by ∅ or { }.
(a) {1, 2}
(b) {0}
(c) ∅
(d) {2, 4, 6}
Answer: (b) {0}
Explanation: A singleton set contains exactly one element. The set {0} has one element, which is 0.
(a) Set of natural numbers
(b) Set of integers
(c) Set of even numbers
(d) Set of months in a year
Answer: (d) Set of months in a year
Explanation: A finite set has a limited number of elements. There are 12 months in a year.
(a) Set of days in a week
(b) Set of letters in English alphabet
(c) Set of natural numbers
(d) Set of vowels
Answer: (c) Set of natural numbers
Explanation: Natural numbers continue endlessly: 1, 2, 3, 4, … . Therefore, the set of natural numbers is infinite.
(a) They have the same number of elements
(b) They have exactly the same elements
(c) They have no common elements
(d) They are both finite
Answer: (b) They have exactly the same elements
Explanation: Equal sets contain exactly the same elements, regardless of order.
(a) A ≠ B
(b) A = B
(c) A ∩ B = ∅
(d) A ⊂ B
Answer: (b) A = B
Explanation: The order of elements does not matter in a set. Both sets contain the same elements.
(a) Equal sets
(b) Equivalent sets
(c) Empty sets
(d) Singleton sets
Answer: (b) Equivalent sets
Explanation: Equivalent sets have the same number of elements. Here both A and B have 3 elements.
(a) Equal sets
(b) Overlapping sets
(c) Disjoint sets
(d) Universal sets
Answer: (c) Disjoint sets
Explanation: Two sets are disjoint if they have no common element.
(a) It has one element
(b) It has no element
(c) It contains zero as an element
(d) It is never a subset of any set
Answer: (b) It has no element
Explanation: The empty set has no elements. It is different from {0}, which contains one element.
(a) A ⊆ B
(b) B ⊆ A
(c) A = B
(d) A ∩ B = ∅
Answer: (a) A ⊆ B
Explanation: Every element of A is also an element of B. Therefore, A is a subset of B.
(a) Only the empty set
(b) Itself
(c) Only the universal set
(d) No set
Answer: (b) Itself
Explanation: Every element of a set belongs to itself. Hence, A ⊆ A for every set A.
(a) No set
(b) Every set
(c) Only itself
(d) Only finite sets
Answer: (b) Every set
Explanation: The empty set has no element that can violate the subset condition. Therefore, ∅ is a subset of every set.
(a) 3
(b) 6
(c) 8
(d) 9
Answer: (c) 8
Explanation: If a set has n elements, then it has 2^n subsets. Here n = 3, so number of subsets = 2^3 = 8.
(a) 4
(b) 8
(c) 15
(d) 16
Answer: (c) 15
Explanation: Number of proper subsets = 2^n − 1. Here n = 4, so proper subsets = 2^4 − 1 = 16 − 1 = 15.
(a) {1}
(b) {2, 3}
(c) {1, 2, 3}
(d) {4}
Answer: (d) {4}
Explanation: The element 4 does not belong to A. Hence, {4} is not a subset of A.
(a) {1, 2, 3}
(b) {1, 2}
(c) {1, 2, 3, 4}
(d) {4}
Answer: (b) {1, 2}
Explanation: A proper subset contains some or all elements of a set, but it cannot be equal to the set itself.
(a) {1, 2}
(b) {{1}, {2}}
(c) {∅, {1}, {2}, {1, 2}}
(d) {∅, 1, 2}
Answer: (c) {∅, {1}, {2}, {1, 2}}
Explanation: The power set is the set of all subsets of a given set.
(a) 3
(b) 6
(c) 8
(d) 9
Answer: (c) 8
Explanation: If n(A) = 3, then n(P(A)) = 2^3 = 8.
(a) ∅
(b) {∅}
(c) {0}
(d) {{0}}
Answer: (b) {∅}
Explanation: The empty set has one subset, which is ∅ itself. Therefore, P(∅) = {∅}.
(a) 4
(b) 5
(c) 16
(d) 32
Answer: (b) 5
Explanation: n(P(A)) = 2^n. Since 2^5 = 32, n(A) = 5.
(a) {1}
(b) {∅, {1}}
(c) {∅, 1}
(d) {{1}}
Answer: (b) {∅, {1}}
Explanation: A singleton set has two subsets: ∅ and the set itself.
(a) 10
(b) 16
(c) 25
(d) 32
Answer: (d) 32
Explanation: Number of subsets = 2^5 = 32.
(a) 4
(b) 8
(c) 12
(d) 16
Answer: (b) 8
Explanation: If one element is fixed in every subset, each of the remaining 3 elements may be included or excluded. So the number of subsets = 2^3 = 8.
(a) 2
(b) 3
(c) 4
(d) 8
Answer: (c) 4
Explanation: Exclude the fixed element. The remaining 2 elements can form 2^2 = 4 subsets.
(a) {3}
(b) {1, 2, 3, 4, 5}
(c) {1, 2}
(d) {4, 5}
Answer: (b) {1, 2, 3, 4, 5}
Explanation: The union of two sets contains all elements present in A or B or both.
(a) {1, 2}
(b) {3}
(c) {4, 5}
(d) {1, 2, 3, 4, 5}
Answer: (b) {3}
Explanation: The intersection contains common elements. The common element in A and B is 3.
(a) {1, 2}
(b) {3, 4}
(c) {5, 6}
(d) {1, 2, 5, 6}
Answer: (a) {1, 2}
Explanation: A − B contains elements that are in A but not in B.
(a) {1, 2}
(b) {3, 4}
(c) {5, 6}
(d) {1, 2, 5, 6}
Answer: (c) {5, 6}
Explanation: B − A contains elements that are in B but not in A.
(a) A
(b) B
(c) ∅
(d) A ∪ B
Answer: (c) ∅
Explanation: Disjoint sets have no common element. Therefore, their intersection is the empty set.
(a) {1, 2, 3, 4, 5, 6}
(b) {2, 4, 6}
(c) {1, 3, 5}
(d) ∅
Answer: (d) ∅
Explanation: A and B have no common elements.
(a) 25
(b) 30
(c) 35
(d) 40
Answer: (b) 30
Explanation: n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 20 + 15 − 5 = 30.
(a) 5
(b) 10
(c) 15
(d) 20
Answer: (a) 5
Explanation: n(A ∩ B) = n(A) + n(B) − n(A ∪ B) = 25 + 20 − 40 = 5.
(a) A
(b) B
(c) ∅
(d) A ∩ B
Answer: (b) B
Explanation: If A is a subset of B, all elements of A are already in B. So A ∪ B = B.
(a) A
(b) B
(c) ∅
(d) A ∪ B
Answer: (a) A
Explanation: Since all elements of A are in B, the common part of A and B is A.
(a) {2, 4, 6}
(b) {1, 3, 5}
(c) {1, 2, 3}
(d) {4, 5, 6}
Answer: (b) {1, 3, 5}
Explanation: A' contains all elements of U that are not in A.
(a) {a, c, e}
(b) {b, d}
(c) {a, b, c}
(d) {d, e}
Answer: (b) {b, d}
Explanation: The elements of U not present in A are b and d.
(a) Universal set
(b) Empty set
(c) Singleton set
(d) Power set
Answer: (b) Empty set
Explanation: The universal set contains all elements under consideration. Therefore, there is no element outside it.
(a) Empty set
(b) Universal set
(c) Singleton set
(d) Power set
Answer: (b) Universal set
Explanation: Since the empty set has no element, all elements of the universal set are outside it.
(a) A
(b) A'
(c) U
(d) ∅
Answer: (c) U
Explanation: A and its complement together contain all elements of the universal set.
(a) A
(b) A'
(c) U
(d) ∅
Answer: (d) ∅
Explanation: A set and its complement have no common element.
(a) A' ∪ B'
(b) A' ∩ B'
(c) A ∩ B
(d) A ∪ B
Answer: (b) A' ∩ B'
Explanation: De Morgan’s first law states that the complement of a union is the intersection of the complements.
(a) A' ∪ B'
(b) A' ∩ B'
(c) A ∩ B
(d) A ∪ B
Answer: (a) A' ∪ B'
Explanation: De Morgan’s second law states that the complement of an intersection is the union of the complements.
(a) A ∪ B
(b) A ∩ B
(c) A ∩ B'
(d) A' ∩ B
Answer: (c) A ∩ B'
Explanation: A − B contains elements that are in A but not in B. This is the same as A ∩ B'.
(a) {1, 2}
(b) {3, 4}
(c) {6}
(d) {1, 2, 5, 6}
Answer: (c) {6}
Explanation: A ∪ B = {1, 2, 3, 4, 5}. The only element of U not in A ∪ B is 6.
(a) 25
(b) 30
(c) 35
(d) 40
Answer: (c) 35
Explanation: n(M ∪ S) = n(M) + n(S) − n(M ∩ S) = 25 + 20 − 10 = 35.
(a) 5
(b) 10
(c) 15
(d) 20
Answer: (a) 5
Explanation: Students who like at least one subject = 35. Therefore, students who like neither = 40 − 35 = 5.
(a) 10
(b) 15
(c) 20
(d) 25
Answer: (b) 15
Explanation: Tea only = n(T) − n(T ∩ C) = 30 − 15 = 15.
(a) 5
(b) 10
(c) 15
(d) 20
Answer: (b) 10
Explanation: Coffee only = n(C) − n(T ∩ C) = 25 − 15 = 10.
(a) 5
(b) 8
(c) 10
(d) 12
Answer: (c) 10
Explanation: n(A ∩ B) = n(A) + n(B) − n(A ∪ B) = 18 + 22 − 30 = 10.
(a) 20
(b) 26
(c) 32
(d) 38
Answer: (b) 26
Explanation: Exactly one = n(A) + n(B) − 2n(A ∩ B) = 20 + 18 − 12 = 26.
(a) 77
(b) 82
(c) 87
(d) 92
Answer: (c) 87
Explanation:
n(C ∪ F ∪ B) = 45 + 40 + 30 − 15 − 10 − 8 + 5 = 87.
(a) 5
(b) 10
(c) 13
(d) 18
Answer: (c) 13
Explanation: Total students = 100. Students who like at least one sport = 87. Therefore, students who like none = 100 − 87 = 13.
(a) 15
(b) 18
(c) 23
(d) 28
Answer: (b) 18
Explanation:
Exactly two = (15 − 5) + (10 − 5) + (8 − 5) = 10 + 5 + 3 = 18.
(a) 22
(b) 27
(c) 32
(d) 37
Answer: (b) 27
Explanation:
Only cricket = 45 − 15 − 8 + 5 = 27.
Reason: The empty set has no element.
(a) Both Assertion and Reason are true, and Reason is the correct explanation
(b) Both Assertion and Reason are true, but Reason is not the correct explanation
(c) Assertion is true, but Reason is false
(d) Assertion is false, but Reason is true
Answer: (a) Both Assertion and Reason are true, and Reason is the correct explanation
Explanation: Since the empty set has no element, there is no element that can fail to belong to another set. Hence, ∅ is a subset of every set.
Reason: The number 0 means nothing.
(a) Both Assertion and Reason are true
(b) Both Assertion and Reason are false
(c) Assertion is false, but Reason is true
(d) Assertion is true, but Reason is false
Answer: (b) Both Assertion and Reason are false
Explanation: {0} is not an empty set. It contains one element, 0. Also, 0 is a number and not “nothing” in set theory.
Reason: A set with n elements has 2^n subsets.
(a) Both Assertion and Reason are true, and Reason is the correct explanation
(b) Both Assertion and Reason are true, but Reason is not the correct explanation
(c) Assertion is true, but Reason is false
(d) Assertion is false, but Reason is true
Answer: (a) Both Assertion and Reason are true, and Reason is the correct explanation
Explanation: A has 3 elements. Therefore, number of subsets = 2^3 = 8.
Reason: Disjoint sets have no common element.
(a) Both Assertion and Reason are true, and Reason is the correct explanation
(b) Both Assertion and Reason are true, but Reason is not the correct explanation
(c) Assertion is true, but Reason is false
(d) Assertion is false, but Reason is true
Answer: (a) Both Assertion and Reason are true, and Reason is the correct explanation
Explanation: The intersection of two sets contains common elements. Since disjoint sets have no common element, their intersection is empty.
Reason: A' contains all elements of U that are not in A.
(a) Both Assertion and Reason are true, and Reason is the correct explanation
(b) Both Assertion and Reason are true, but Reason is not the correct explanation
(c) Assertion is true, but Reason is false
(d) Assertion is false, but Reason is true
Answer: (a) Both Assertion and Reason are true, and Reason is the correct explanation
Explanation: A and A' together include all elements of the universal set U.
In a school, 60 students participated in a survey about the games they like.
32 students like cricket, 28 students like football, and 12 students like both cricket and football.
Answer the following questions based on the given information.
(a) 12
(b) 20
(c) 28
(d) 32
Answer: (b) 20
Explanation: Cricket only = 32 − 12 = 20.
(a) 12
(b) 16
(c) 20
(d) 28
Answer: (b) 16
Explanation: Football only = 28 − 12 = 16.
(a) 36
(b) 40
(c) 48
(d) 60
Answer: (c) 48
Explanation: n(C ∪ F) = 32 + 28 − 12 = 48.
(a) 8
(b) 10
(c) 12
(d) 16
Answer: (c) 12
Explanation: Total students = 60. Students who like at least one game = 48. Therefore, students who like neither = 60 − 48 = 12.
(a) n(A ∩ B) = n(A) + n(B)
(b) n(A ∪ B) = n(A) + n(B) − n(A ∩ B)
(c) n(A − B) = n(A) + n(B)
(d) n(A') = n(A)
Answer: (b) n(A ∪ B) = n(A) + n(B) − n(A ∩ B)
Explanation: This is the standard formula for the union of two finite sets.
| Q No. | Answer | Q No. | Answer |
| 1 | C | 41 | B |
| 2 | B | 42 | B |
| 3 | C | 43 | A |
| 4 | B | 44 | C |
| 5 | A | 45 | C |
| 6 | C | 46 | D |
| 7 | C | 47 | B |
| 8 | B | 48 | A |
| 9 | B | 49 | B |
| 10 | B | 50 | A |
| 11 | A | 51 | B |
| 12 | B | 52 | B |
| 13 | A | 53 | B |
| 14 | B | 54 | B |
| 15 | B | 55 | C |
| 16 | B | 56 | D |
| 17 | C | 57 | B |
| 18 | B | 58 | A |
| 19 | D | 59 | C |
| 20 | C | 60 | C |
| 21 | B | 61 | C |
| 22 | B | 62 | A |
| 23 | B | 63 | B |
| 24 | C | 64 | B |
| 25 | B | 65 | C |
| 26 | A | 66 | B |
| 27 | B | 67 | C |
| 28 | B | 68 | C |
| 29 | C | 69 | B |
| 30 | C | 70 | B |
| 31 | D | 71 | A |
| 32 | B | 72 | B |
| 33 | C | 73 | A |
| 34 | C | 74 | A |
| 35 | B | 75 | A |
| 36 | B | 76 | B |
| 37 | B | 77 | B |
| 38 | D | 78 | C |
| 39 | B | 79 | C |
| 40 | C | 80 | B |
The empty set ∅ has no element.
The set {0} has one element, which is 0.
Therefore, ∅ ≠ {0}.
In a set, repeated elements are written only once.
For example:
The set of letters in “APPLE” is {A, P, L, E}, not {A, P, P, L, E}.
The complement of a set always depends on the universal set.
For example:
If U = {1, 2, 3, 4, 5} and A = {1, 2}, then A' = {3, 4, 5}.
A ∪ B means elements in A or B or both.
A ∩ B means elements common to both A and B.
If a set has n elements, then the number of subsets is 2^n, not 2n.
For example:
If A has 4 elements, number of subsets = 2^4 = 16.
Every set is a subset of itself, but no set is a proper subset of itself.
For example:
If A = {1, 2, 3}, then A ⊆ A is true, but A ⊂ A is false.
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Sets MCQ Questions are multiple choice questions based on the chapter Sets. These questions test concepts such as types of sets, subsets, power sets, union, intersection, complement, and Venn diagrams.
Yes, these MCQs are useful for Class 11 Maths Chapter 1 revision. They cover important concepts from the Sets chapter and help students prepare for school exams and objective-type tests.
If a set has n elements, then the number of subsets is 2^n.
For example, if a set has 3 elements, then the number of subsets is 2^3 = 8.
The power set of a set is the set of all possible subsets of that set.
For example, if A = {1, 2}, then P(A) = {∅, {1}, {2}, {1, 2}}.
∅ is an empty set with no element.
{0} is a singleton set containing one element, 0.
Therefore, ∅ and {0} are not equal.
The formula for the union of two finite sets is:
n(A ∪ B) = n(A) + n(B) − n(A ∩ B)
This formula is commonly used in Venn diagram questions.
De Morgan’s laws are:
(A ∪ B)' = A' ∩ B'
(A ∩ B)' = A' ∪ B'
These laws are used to find complements of union and intersection of sets.
If every element of A is also an element of B, then A is a subset of B.
If A is a subset of B but A is not equal to B, then A is a proper subset of B.
A set with 4 elements has 2^4 − 1 proper subsets.
So, number of proper subsets = 16 − 1 = 15.
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