If \(A=\{x\in\mathbb{N}:x\le 10\}\), \(B=\{x\in\mathbb{N}:x\text{ is odd}\}\), and \(C=\{x\in\mathbb{N}:x\text{ is prime}\}\), what is \(A\cap(B\setminus C)\)?
Answer and explanation
Correct answer: \(\{1,9\}\)
Within the natural numbers up to 10, the odd numbers are \(1,3,5,7,9\). The odd prime numbers in this range are 3, 5, and 7. Subtracting C from B removes these primes and leaves \(B\setminus C=\{1,9\}\). Both 1 and 9 satisfy the definition of A, so intersecting with A does not remove either element. Therefore, \(A\cap(B\setminus C)=\{1,9\}\). Remember that 1 is neither prime nor composite.
Frequently asked questions
What is the correct answer to this question?
\(\{1,9\}\)
Why is this the correct answer?
Within the natural numbers up to 10, the odd numbers are \(1,3,5,7,9\). The odd prime numbers in this range are 3, 5, and 7. Subtracting C from B removes these primes and leaves \(B\setminus C=\{1,9\}\). Both 1 and 9 satisfy the definition of A, so intersecting with A does not remove either element. Therefore, \(A\cap(B\setminus C)=\{1,9\}\). Remember that 1 is neither prime nor composite.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
