If \(A=\{1,3,5,7,9,11\}\), \(B=\{3,6,9,12\}\), and \(C=\{5,9,13\}\), what is the value of \((A\setminus B)\cap C\)?
Answer and explanation
Correct answer: \(\{5\}\)
The difference \(A\setminus B\) consists of elements in \(A\) that are not in \(B\). Removing 3 and 9 from \(A\) gives \(A\setminus B=\{1,5,7,11\}\). Now intersect this result with \(C=\{5,9,13\}\). The only common element is 5, so \((A\setminus B)\cap C=\{5\}\). Although 9 belongs to both \(A\) and \(C\), it is removed because it belongs to \(B\).
Frequently asked questions
What is the correct answer to this question?
\(\{5\}\)
Why is this the correct answer?
The difference \(A\setminus B\) consists of elements in \(A\) that are not in \(B\). Removing 3 and 9 from \(A\) gives \(A\setminus B=\{1,5,7,11\}\). Now intersect this result with \(C=\{5,9,13\}\). The only common element is 5, so \((A\setminus B)\cap C=\{5\}\). Although 9 belongs to both \(A\) and \(C\), it is removed because it belongs to \(B\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
