If U = {1, 2, ..., 120}, A is the set of multiples of 8 and B is the set of multiples of 12, what is n((A ∪ B)')?
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Answer and explanation
Correct answer: 100
There are floor(120/8) = 15 multiples of 8 and floor(120/12) = 10 multiples of 12. Numbers counted in both sets are multiples of lcm(8, 12) = 24, and there are floor(120/24) = 5 of them. Thus n(A ∪ B) = 15 + 10 − 5 = 20. The complement within U therefore has 120 − 20 = 100 elements. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
100
Why is this the correct answer?
There are floor(120/8) = 15 multiples of 8 and floor(120/12) = 10 multiples of 12. Numbers counted in both sets are multiples of lcm(8, 12) = 24, and there are floor(120/24) = 5 of them. Thus n(A ∪ B) = 15 + 10 − 5 = 20. The complement within U therefore has 120 − 20 = 100 elements. Hence 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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