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Subjects
Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)MediumLevel 14

U = {1, 2, 3, ..., 36}, A = {x : x is divisible by 2}, and B = {x : x is divisible by 3}. What is n(A ∩ B)?

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Answer and explanation

Correct answer: 6

A number in A ∩ B must be divisible by both 2 and 3. Such numbers are multiples of lcm(2, 3) = 6. Within U, the multiples are 6, 12, 18, 24, 30, and 36. There are 36 ÷ 6 = 6 such numbers, so n(A ∩ B) = 6. The other choices count a different set or do not use the common condition.

Tags

setsintersectiondivisibilityLCMOperations on Sets (UnionDifference)operations on sets union intersection differenceMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

6

Why is this the correct answer?

A number in A ∩ B must be divisible by both 2 and 3. Such numbers are multiples of lcm(2, 3) = 6. Within U, the multiples are 6, 12, 18, 24, 30, and 36. There are 36 ÷ 6 = 6 such numbers, so n(A ∩ B) = 6. The other choices count a different set or do not use the common condition.

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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