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Class 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 20

If U = {1, 2, …, 96}, A = {x : x is divisible by 6}, and B = {x : x is divisible by 8}, what is |(A ∪ B)′|?

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Answer and explanation

Correct answer: 72

There are floor(96/6) = 16 multiples of 6 and floor(96/8) = 12 multiples of 8. Numbers counted in both sets are multiples of lcm(6,8) = 24, giving floor(96/24) = 4. Hence |A ∪ B| = 16 + 12 − 4 = 24. The complement therefore has 96 − 24 = 72 elements, so option C is correct.

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setscomplementunioninclusion-exclusionComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

72

Why is this the correct answer?

There are floor(96/6) = 16 multiples of 6 and floor(96/8) = 12 multiples of 8. Numbers counted in both sets are multiples of lcm(6,8) = 24, giving floor(96/24) = 4. Hence |A ∪ B| = 16 + 12 − 4 = 24. The complement therefore has 96 − 24 = 72 elements, so option C is correct.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.

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