U = {1, 2, 3, ..., 72}, A = {x : x is divisible by 6}, and B = {x : x is divisible by 8}. What is n(A ∪ B)?
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Answer and explanation
Correct answer: 18
Use the inclusion–exclusion formula n(A ∪ B) = n(A) + n(B) − n(A ∩ B). There are 72 ÷ 6 = 12 multiples of 6 and 72 ÷ 8 = 9 multiples of 8. The common multiples are multiples of lcm(6, 8) = 24, giving 72 ÷ 24 = 3. Thus n(A ∪ B) = 12 + 9 − 3 = 18, so B is correct.
Frequently asked questions
What is the correct answer to this question?
18
Why is this the correct answer?
Use the inclusion–exclusion formula n(A ∪ B) = n(A) + n(B) − n(A ∩ B). There are 72 ÷ 6 = 12 multiples of 6 and 72 ÷ 8 = 9 multiples of 8. The common multiples are multiples of lcm(6, 8) = 24, giving 72 ÷ 24 = 3. Thus n(A ∪ B) = 12 + 9 − 3 = 18, so B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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