If \(A=\{1,2,3,4,5,6\}\), \(B=\{2,3,5,7\}\), and \(C=\{3,4,5,8\}\), what is \((A\setminus B)\cap C\)?
Answer and explanation
Correct answer: \(\{4\}\)
The difference \(A\setminus B\) contains elements that are in \(A\) but not in \(B\). Removing 2, 3, and 5 from \(A\) gives \(\{1,4,6\}\). Now intersect this result with \(C=\{3,4,5,8\}\). The only common element is 4, so \((A\setminus B)\cap C=\{4\}\). Option C stops after the difference operation, and option D incorrectly includes 8.
Frequently asked questions
What is the correct answer to this question?
\(\{4\}\)
Why is this the correct answer?
The difference \(A\setminus B\) contains elements that are in \(A\) but not in \(B\). Removing 2, 3, and 5 from \(A\) gives \(\{1,4,6\}\). Now intersect this result with \(C=\{3,4,5,8\}\). The only common element is 4, so \((A\setminus B)\cap C=\{4\}\). Option C stops after the difference operation, and option D incorrectly includes 8.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
