If \(A=\{1,2,3,4,5,6\}\), \(B=\{2,4,6\}\), and \(C=\{1,3,5\}\), what is the value of \((A-B)\cap C\)?
Answer and explanation
Correct answer: \(\{1,3,5\}\)
First evaluate the difference \(A-B\). Remove every element of \(B\), namely 2, 4, and 6, from \(A\); this gives \(A-B=\{1,3,5\}\). Now intersect this result with \(C\). Since \(C=\{1,3,5\}\), every element of \(A-B\) is also in \(C\). Hence \((A-B)\cap C=\{1,3,5\}\). Difference removes the second set’s elements, while intersection retains only common elements.
Frequently asked questions
What is the correct answer to this question?
\(\{1,3,5\}\)
Why is this the correct answer?
First evaluate the difference \(A-B\). Remove every element of \(B\), namely 2, 4, and 6, from \(A\); this gives \(A-B=\{1,3,5\}\). Now intersect this result with \(C\). Since \(C=\{1,3,5\}\), every element of \(A-B\) is also in \(C\). Hence \((A-B)\cap C=\{1,3,5\}\). Difference removes the second set’s elements, while intersection retains only common elements.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
