If \(A=\{x:x\in\mathbb{N},x\le 6\}\) and \(B=\{x:x\in\mathbb{N},x\text{ is even},x\le 8\}\), what is \(A\cap B\)?
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Answer and explanation
Correct answer: \(\{2,4,6\}\)
Assuming the standard school convention \(\mathbb{N}=\{1,2,3,\ldots\}\), we have \(A=\{1,2,3,4,5,6\}\). The even natural numbers not exceeding 8 are \(B=\{2,4,6,8\}\). The common elements are 2, 4, and 6, so \(A\cap B=\{2,4,6\}\). The element 8 is excluded because it is not in A.
Frequently asked questions
What is the correct answer to this question?
\(\{2,4,6\}\)
Why is this the correct answer?
Assuming the standard school convention \(\mathbb{N}=\{1,2,3,\ldots\}\), we have \(A=\{1,2,3,4,5,6\}\). The even natural numbers not exceeding 8 are \(B=\{2,4,6,8\}\). The common elements are 2, 4, and 6, so \(A\cap B=\{2,4,6\}\). The element 8 is excluded because it is not in A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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