Assume that \(\mathbb{N}=\{1,2,3,\ldots\}\). If \(A=\{x\in\mathbb{N}\mid x\le 12\}\) and \(B=\{x\in\mathbb{N}\mid x\text{ is prime}\}\), with \(B\) restricted to \(A\), what is \(A\setminus B\)?
Answer and explanation
Correct answer: \(\{1,4,6,8,9,10,12\}\)
Since the natural numbers begin at 1 and A is restricted by \(x\le 12\), we have \(A=\{1,2,3,4,5,6,7,8,9,10,11,12\}\). The primes in this range are \(B=\{2,3,5,7,11\}\). Removing these from A leaves \(\{1,4,6,8,9,10,12\}\). Number 1 is included because it is neither prime nor composite; it has exactly one positive divisor.
Frequently asked questions
What is the correct answer to this question?
\(\{1,4,6,8,9,10,12\}\)
Why is this the correct answer?
Since the natural numbers begin at 1 and A is restricted by \(x\le 12\), we have \(A=\{1,2,3,4,5,6,7,8,9,10,11,12\}\). The primes in this range are \(B=\{2,3,5,7,11\}\). Removing these from A leaves \(\{1,4,6,8,9,10,12\}\). Number 1 is included because it is neither prime nor composite; it has exactly one positive divisor.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
