If U = {1,2,3,…,60} and A = {x ∈ U : 6 divides x}, what is n(Aᶜ)?
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Answer and explanation
Correct answer: 50
The elements of A are the positive multiples of 6 not exceeding 60: 6, 12, 18, …, 60. Their number is 60 ÷ 6 = 10. Since U has 60 elements, the complement Aᶜ contains all elements of U that are not divisible by 6. Hence n(Aᶜ) = n(U) − n(A) = 60 − 10 = 50. Therefore, option A is correct; option B counts A itself.
Frequently asked questions
What is the correct answer to this question?
50
Why is this the correct answer?
The elements of A are the positive multiples of 6 not exceeding 60: 6, 12, 18, …, 60. Their number is 60 ÷ 6 = 10. Since U has 60 elements, the complement Aᶜ contains all elements of U that are not divisible by 6. Hence n(Aᶜ) = n(U) − n(A) = 60 − 10 = 50. Therefore, option A is correct; option B counts A itself.
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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