If \(A=\{1,2,3,4,5\}\), \(B=\{2,5\}\), and \(C=\{5,6\}\), what is \((A-B)\cap C\)?
Answer and explanation
Correct answer: \(\varnothing\)
First calculate the difference. Since 2 and 5 are the elements of B that occur in A, they must be removed: \(A-B=\{1,3,4\}\). The next operation is intersection with \(C=\{5,6\}\). None of 1, 3, or 4 is present in C, so there is no common element. Hence \((A-B)\cap C=\varnothing\), making option A correct. Option B wrongly keeps 5 even though it was removed, while option D is not in \(A-B\).
Frequently asked questions
What is the correct answer to this question?
\(\varnothing\)
Why is this the correct answer?
First calculate the difference. Since 2 and 5 are the elements of B that occur in A, they must be removed: \(A-B=\{1,3,4\}\). The next operation is intersection with \(C=\{5,6\}\). None of 1, 3, or 4 is present in C, so there is no common element. Hence \((A-B)\cap C=\varnothing\), making option A correct. Option B wrongly keeps 5 even though it was removed, while option D is not in \(A-B\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
