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Class 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 9

If U = {x : x ∈ ℕ, x ≤ 20} and A is the set of positive divisors of 20, what is n(A′)?

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Answer and explanation

Correct answer: 14

Taking ℕ as the positive natural numbers, U = {1,2,...,20}, so n(U) = 20. The positive divisors of 20 are 1, 2, 4, 5, 10, and 20, giving n(A) = 6. The complement A′ contains the members of U that are not divisors of 20. Hence n(A′) = 20 − 6 = 14, so option C is correct.

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setscomplementdivisorsuniversal setComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

14

Why is this the correct answer?

Taking ℕ as the positive natural numbers, U = {1,2,...,20}, so n(U) = 20. The positive divisors of 20 are 1, 2, 4, 5, 10, and 20, giving n(A) = 6. The complement A′ contains the members of U that are not divisors of 20. Hence n(A′) = 20 − 6 = 14, 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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