If \(U=\mathbb{N}\) and \(A=\{x:x\in\mathbb{N},\ x\le 100\}\), what is \(A'\)?
Answer and explanation
Correct answer: \(\{x:x\in\mathbb{N},\ x>100\}\)
The complement is always determined relative to the stated universal set. Here \(U=\mathbb{N}\), and \(A\) contains every natural number less than or equal to 100. Consequently, the natural numbers not belonging to \(A\) are exactly those greater than 100: \(A'=\mathbb{N}\setminus A=\{x\in\mathbb{N}:x>100\}\). This is an infinite set, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(\{x:x\in\mathbb{N},\ x>100\}\)
Why is this the correct answer?
The complement is always determined relative to the stated universal set. Here \(U=\mathbb{N}\), and \(A\) contains every natural number less than or equal to 100. Consequently, the natural numbers not belonging to \(A\) are exactly those greater than 100: \(A'=\mathbb{N}\setminus A=\{x\in\mathbb{N}:x>100\}\). This is an infinite set, so 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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