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Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)MediumLevel 15

Let U = {1, 2, ..., 96}. If A is the set of multiples of 6 in U and B is the set of multiples of 10 in U, what is n(A ∪ B)?

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Answer and explanation

Correct answer: 22

The multiples of 6 from 1 to 96 are counted by ⌊96/6⌋ = 16. The multiples of 10 are counted by ⌊96/10⌋ = 9. Common elements are multiples of lcm(6,10) = 30, and there are ⌊96/30⌋ = 3 of them. Therefore, n(A ∪ B) = 16 + 9 − 3 = 22, by inclusion–exclusion. Thus option A is correct.

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setsunioninclusion-exclusionmultiplesOperations on Sets (UnionIntersectionDifference)operations on sets union intersection differenceMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

22

Why is this the correct answer?

The multiples of 6 from 1 to 96 are counted by ⌊96/6⌋ = 16. The multiples of 10 are counted by ⌊96/10⌋ = 9. Common elements are multiples of lcm(6,10) = 30, and there are ⌊96/30⌋ = 3 of them. Therefore, n(A ∪ B) = 16 + 9 − 3 = 22, by inclusion–exclusion. 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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