If U = {1, 2, ..., 36} and A = {x : x ∈ U and x is not prime}, how many elements are in A'?
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Answer and explanation
Correct answer: 11
A contains all non-prime numbers in U. Therefore, its complement A' contains exactly the prime numbers from 1 to 36. These primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31. There are 11 such numbers. Note that 1 is neither prime nor composite, but it still belongs to A because it is not prime.
Frequently asked questions
What is the correct answer to this question?
11
Why is this the correct answer?
A contains all non-prime numbers in U. Therefore, its complement A' contains exactly the prime numbers from 1 to 36. These primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31. There are 11 such numbers. Note that 1 is neither prime nor composite, but it still belongs to A because it is not prime.
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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