If U = {x ∈ N : x ≤ 15} and M = {5, 10, 15}, how many elements are in M′?
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Answer and explanation
Correct answer: 12
The universal set U contains the natural numbers 1 through 15, so n(U) = 15. Set M contains exactly three distinct elements: 5, 10, and 15, so n(M) = 3. Because M is a subset of U, the number of elements in its complement is n(M′) = n(U) − n(M) = 15 − 3 = 12. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
The universal set U contains the natural numbers 1 through 15, so n(U) = 15. Set M contains exactly three distinct elements: 5, 10, and 15, so n(M) = 3. Because M is a subset of U, the number of elements in its complement is n(M′) = n(U) − n(M) = 15 − 3 = 12. Hence option A 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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