Let U = {1, 2, ..., 90}. If A is the set of multiples of 5 and B is the set of multiples of 9, what is n(A ∪ B)?
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Answer and explanation
Correct answer: 26
There are floor(90/5) = 18 multiples of 5 and floor(90/9) = 10 multiples of 9. Numbers counted in both sets are multiples of lcm(5, 9) = 45; within 1 to 90 these are 45 and 90, so there are 2. By inclusion-exclusion, n(A ∪ B) = 18 + 10 − 2 = 26. Thus option A is correct.
Frequently asked questions
What is the correct answer to this question?
26
Why is this the correct answer?
There are floor(90/5) = 18 multiples of 5 and floor(90/9) = 10 multiples of 9. Numbers counted in both sets are multiples of lcm(5, 9) = 45; within 1 to 90 these are 45 and 90, so there are 2. By inclusion-exclusion, n(A ∪ B) = 18 + 10 − 2 = 26. Thus option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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