Let U = {x : x ∈ N, x ≤ 30} and let A be the set of positive divisors of 30 in U. What is n(A')?
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Answer and explanation
Correct answer: 22
The universal set U contains the natural numbers 1 through 30, so n(U) = 30. The positive divisors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30, giving n(A) = 8. The complement A' contains all elements of U that are not in A. Thus n(A') = n(U) − n(A) = 30 − 8 = 22. Hence option C is correct.
Frequently asked questions
What is the correct answer to this question?
22
Why is this the correct answer?
The universal set U contains the natural numbers 1 through 30, so n(U) = 30. The positive divisors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30, giving n(A) = 8. The complement A' contains all elements of U that are not in A. Thus n(A') = n(U) − n(A) = 30 − 8 = 22. Hence 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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