If U = {1, 2, ..., 96}, A is the set of multiples of 6 and B is the set of multiples of 10, then what is n(A ∪ B)?
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Answer and explanation
Correct answer: 22
Between 1 and 96, the number of multiples of 6 is floor(96/6) = 16, and the number of multiples of 10 is floor(96/10) = 9. Elements divisible by both 6 and 10 are multiples of lcm(6,10) = 30; there are floor(96/30) = 3. By inclusion–exclusion, n(A ∪ B) = 16 + 9 − 3 = 22.
Frequently asked questions
What is the correct answer to this question?
22
Why is this the correct answer?
Between 1 and 96, the number of multiples of 6 is floor(96/6) = 16, and the number of multiples of 10 is floor(96/10) = 9. Elements divisible by both 6 and 10 are multiples of lcm(6,10) = 30; there are floor(96/30) = 3. By inclusion–exclusion, n(A ∪ B) = 16 + 9 − 3 = 22.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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