If K = {x : x ∈ N, x < 40 and x has exactly three positive divisors}, what is K?
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Answer and explanation
Correct answer: K = {4, 9, 25}
A positive integer has exactly three positive divisors precisely when it is the square of a prime: if x = p², its divisors are 1, p, and p². The prime squares less than 40 are 2² = 4, 3² = 9, and 5² = 25. The next prime square, 7² = 49, is not less than 40. Hence K = {4, 9, 25}.
Frequently asked questions
What is the correct answer to this question?
K = {4, 9, 25}
Why is this the correct answer?
A positive integer has exactly three positive divisors precisely when it is the square of a prime: if x = p², its divisors are 1, p, and p². The prime squares less than 40 are 2² = 4, 3² = 9, and 5² = 25. The next prime square, 7² = 49, is not less than 40. Hence K = {4, 9, 25}.
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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