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

If U = {1, 2, ..., 105}, A is the set of multiples of 7 and B is the set of multiples of 15, what is n(A ∩ B)?

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Answer and explanation

Correct answer: 1

An element in A ∩ B must be divisible by both 7 and 15. Because 7 and 15 are coprime, their least common multiple is 7 × 15 = 105. The positive multiples of 105 not exceeding 105 consist only of 105 itself. Therefore A ∩ B = {105}, and its cardinality is n(A ∩ B) = 1. Hence option A is correct.

Tags

setsintersectionleast-common-multiplemultiplesOperations on Sets (UnionDifference)operations on sets union intersection differenceMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

1

Why is this the correct answer?

An element in A ∩ B must be divisible by both 7 and 15. Because 7 and 15 are coprime, their least common multiple is 7 × 15 = 105. The positive multiples of 105 not exceeding 105 consist only of 105 itself. Therefore A ∩ B = {105}, and its cardinality is n(A ∩ B) = 1. Hence 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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