If \(U=\{1,2,\ldots,40\}\), \(A\) is the set of prime numbers, and \(B\) is the set of odd numbers, what is \(|A'\cap B|\)?
Answer and explanation
Correct answer: 10
The set \(B\) contains the 20 odd numbers from 1 through 40. The odd prime numbers in this range are 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31, giving 10 elements. Notice that 1 is odd but not prime, while 2 is prime but not odd. Therefore, the odd numbers that are not prime, namely \(A'\cap B\), number \(20-10=10\).
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
The set \(B\) contains the 20 odd numbers from 1 through 40. The odd prime numbers in this range are 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31, giving 10 elements. Notice that 1 is odd but not prime, while 2 is prime but not odd. Therefore, the odd numbers that are not prime, namely \(A'\cap B\), number \(20-10=10\).
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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