If U = {x : x ∈ N, 1 ≤ x ≤ 30} and A = {x ∈ U : x is divisible by both 2 and 3}, what is n(Aᶜ)?
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Answer and explanation
Correct answer: 25
A number divisible by both 2 and 3 must be divisible by their least common multiple, 6. Between 1 and 30, the multiples of 6 are 6, 12, 18, 24, and 30, so n(A) = 5. The universal set has 30 elements, and Aᶜ contains all remaining elements. Therefore n(Aᶜ) = 30 − 5 = 25, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
25
Why is this the correct answer?
A number divisible by both 2 and 3 must be divisible by their least common multiple, 6. Between 1 and 30, the multiples of 6 are 6, 12, 18, 24, and 30, so n(A) = 5. The universal set has 30 elements, and Aᶜ contains all remaining elements. Therefore n(Aᶜ) = 30 − 5 = 25, so option B 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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