If \(A=\{x:x\in\mathbb{N},\ 1\le x\le 10\}\), \(B=\{1,4,7,10\}\), and \(C=\{2,4,6,8,10\}\), what is \(A\setminus(B\cup C)\)?
Answer and explanation
Correct answer: \(\{3,5,9\}\)
Since A contains the natural numbers from 1 through 10, write \(A=\{1,2,3,4,5,6,7,8,9,10\}\). First calculate the union: \(B\cup C=\{1,2,4,6,7,8,10\}\). Remove these union elements from A. The numbers left are 3, 5, and 9, so \(A\setminus(B\cup C)=\{3,5,9\}\). Option B is the removed union, not the required difference.
Frequently asked questions
What is the correct answer to this question?
\(\{3,5,9\}\)
Why is this the correct answer?
Since A contains the natural numbers from 1 through 10, write \(A=\{1,2,3,4,5,6,7,8,9,10\}\). First calculate the union: \(B\cup C=\{1,2,4,6,7,8,10\}\). Remove these union elements from A. The numbers left are 3, 5, and 9, so \(A\setminus(B\cup C)=\{3,5,9\}\). Option B is the removed union, not the required difference.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
