If \(U=\{x:x\in\mathbb N, x\le 50\}\) and \(A=\{x:x\text{ is not a prime number}\}\), then \(A'\) is the set of what?
Answer and explanation
Correct answer: Prime numbers
The universal set contains the natural numbers from 1 through 50. Set \(A\) consists of all numbers in this universe that are not prime. Its complement therefore contains exactly those members that are prime. Notice that 1 is not prime, so it remains in \(A\) and is not included in \(A'\). Thus option A is correct.
Frequently asked questions
What is the correct answer to this question?
Prime numbers
Why is this the correct answer?
The universal set contains the natural numbers from 1 through 50. Set \(A\) consists of all numbers in this universe that are not prime. Its complement therefore contains exactly those members that are prime. Notice that 1 is not prime, so it remains in \(A\) and is not included in \(A'\). Thus option A is correct.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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