In a class, U is the set of all students and A is the set of students who like mathematics. If n(U) = 55 and n(A) = 37, how many students do not like mathematics, that is, n(Aᶜ)?
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Answer and explanation
Correct answer: 18
Students who do not like mathematics form the complement Aᶜ of A. When A is a subset of the universal set U, the cardinality rule is n(Aᶜ) = n(U) - n(A). Substituting the given values gives n(Aᶜ) = 55 - 37 = 18. Thus 18 students do not like mathematics; 37 is the size of A and 55 is the total class size.
Frequently asked questions
What is the correct answer to this question?
18
Why is this the correct answer?
Students who do not like mathematics form the complement Aᶜ of A. When A is a subset of the universal set U, the cardinality rule is n(Aᶜ) = n(U) - n(A). Substituting the given values gives n(Aᶜ) = 55 - 37 = 18. Thus 18 students do not like mathematics; 37 is the size of A and 55 is the total class size.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
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