Which is the set C₃ = {x ∈ ℕ : x is a factor of 9 and x is prime}?
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Answer and explanation
Correct answer: {3}
The positive natural-number factors of 9 are 1, 3, and 9. Among them, 3 is prime because it has exactly two positive divisors, 1 and 3. The number 1 is not prime, and 9 is composite because it has more than two positive divisors. Therefore, the set C₃ contains only 3, so C₃ = {3}.
Frequently asked questions
What is the correct answer to this question?
{3}
Why is this the correct answer?
The positive natural-number factors of 9 are 1, 3, and 9. Among them, 3 is prime because it has exactly two positive divisors, 1 and 3. The number 1 is not prime, and 9 is composite because it has more than two positive divisors. Therefore, the set C₃ contains only 3, so C₃ = {3}.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
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