If \(A=\{x:x\in\mathbb N,\ x\le12\}\) and \(B=\{x:x\in\mathbb N,\ x\text{ is a perfect square},\ x\le12\}\), how many elements are in \(A-B\)?
Answer and explanation
Correct answer: 9
Using the convention \(\mathbb N=\{1,2,3,\ldots\}\), the set \(A=\{1,2,\ldots,12\}\) has 12 elements. The perfect squares not exceeding 12 are \(B=\{1,4,9\}\), which has 3 elements. Removing these three elements from \(A\) leaves \(|A-B|=12-3=9\). Thus option B is correct; option C would incorrectly ignore the subtraction.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
Using the convention \(\mathbb N=\{1,2,3,\ldots\}\), the set \(A=\{1,2,\ldots,12\}\) has 12 elements. The perfect squares not exceeding 12 are \(B=\{1,4,9\}\), which has 3 elements. Removing these three elements from \(A\) leaves \(|A-B|=12-3=9\). Thus option B is correct; option C would incorrectly ignore the subtraction.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
