If \(U=\{x:x\in\mathbb N, x\le 35\}\) and \(A=\{x:x\text{ is a composite number}\}\), what type of elements will be in \(A'\)?
Answer and explanation
Correct answer: 1 and prime numbers
The complement \(A'\) contains all members of the universal set that are not composite. Among natural numbers, every number greater than 1 is either prime or composite, while 1 is neither prime nor composite. Therefore, within \(1\) to \(35\), \(A'\) consists of 1 together with all prime numbers. Option A is complete.
Frequently asked questions
What is the correct answer to this question?
1 and prime numbers
Why is this the correct answer?
The complement \(A'\) contains all members of the universal set that are not composite. Among natural numbers, every number greater than 1 is either prime or composite, while 1 is neither prime nor composite. Therefore, within \(1\) to \(35\), \(A'\) consists of 1 together with all prime numbers. Option A is complete.
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.
