If \(A=\{x:x\in\mathbb{N},x^2\le 49\}\) and \(B=\{2,4,6,8\}\), what is \(A\setminus B\)?
Answer and explanation
Correct answer: \{1,3,5,7\}
Since \(x\) is a natural number and \(x^2\le49\), the possible values are \(1,2,3,4,5,6,7\). Thus, \(A=\{1,2,3,4,5,6,7\}\). The difference \(A\setminus B\) contains elements that belong to A but do not belong to B. Removing 2, 4, and 6 from A leaves \(\{1,3,5,7\}\). The element 8 in B is irrelevant because it is not in A. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
\{1,3,5,7\}
Why is this the correct answer?
Since \(x\) is a natural number and \(x^2\le49\), the possible values are \(1,2,3,4,5,6,7\). Thus, \(A=\{1,2,3,4,5,6,7\}\). The difference \(A\setminus B\) contains elements that belong to A but do not belong to B. Removing 2, 4, and 6 from A leaves \(\{1,3,5,7\}\). The element 8 in B is irrelevant because it is not in A. Therefore, option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
