If U = {x : x ∈ ℕ, x ≤ 48}, A = {x ∈ U : 4 divides x}, and B = {x ∈ U : 6 divides x}, what is n((A ∪ B)′)?
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Answer and explanation
Correct answer: 32
Assuming ℕ begins at 1, U has 48 elements. There are 12 multiples of 4 and 8 multiples of 6 up to 48. Their common elements are multiples of lcm(4,6) = 12, namely 4 numbers: 12, 24, 36, and 48. Hence n(A ∪ B) = 12 + 8 − 4 = 16. Therefore n((A ∪ B)′) = 48 − 16 = 32.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
Assuming ℕ begins at 1, U has 48 elements. There are 12 multiples of 4 and 8 multiples of 6 up to 48. Their common elements are multiples of lcm(4,6) = 12, namely 4 numbers: 12, 24, 36, and 48. Hence n(A ∪ B) = 12 + 8 − 4 = 16. Therefore n((A ∪ B)′) = 48 − 16 = 32.
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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