Let U = {x ∈ N : x ≤ 15} and A = {x ∈ U : x is not prime}. What is A′, the complement of A in U?
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Answer and explanation
Correct answer: {2, 3, 5, 7, 11, 13}
The universal set consists of the natural numbers from 1 through 15. Set A contains all non-prime numbers, including 1, because 1 is neither prime nor composite. Therefore, the complement A′ contains exactly the prime numbers in U: 2, 3, 5, 7, 11, and 13. Thus option A is correct.
Frequently asked questions
What is the correct answer to this question?
{2, 3, 5, 7, 11, 13}
Why is this the correct answer?
The universal set consists of the natural numbers from 1 through 15. Set A contains all non-prime numbers, including 1, because 1 is neither prime nor composite. Therefore, the complement A′ contains exactly the prime numbers in U: 2, 3, 5, 7, 11, and 13. Thus 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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