If U = {1,2,3,…,40} and A = {x ∈ U : x is divisible by 4 or 5}, what is n(Aᶜ)?
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Answer and explanation
Correct answer: 24
Among the integers from 1 to 40, there are 40/4 = 10 multiples of 4 and 40/5 = 8 multiples of 5. Multiples of both 4 and 5 are multiples of 20, and there are 40/20 = 2 of them. By inclusion–exclusion, n(A) = 10 + 8 − 2 = 16. Therefore, n(Aᶜ) = n(U) − n(A) = 40 − 16 = 24, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
24
Why is this the correct answer?
Among the integers from 1 to 40, there are 40/4 = 10 multiples of 4 and 40/5 = 8 multiples of 5. Multiples of both 4 and 5 are multiples of 20, and there are 40/20 = 2 of them. By inclusion–exclusion, n(A) = 10 + 8 − 2 = 16. Therefore, n(Aᶜ) = n(U) − n(A) = 40 − 16 = 24, so option A is correct.
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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