If \(A\) and \(B\) are finite sets, which is the correct formula for \(n(A\setminus B)\)?
Answer and explanation
Correct answer: \(n(A)-n(A\cap B)\)
The set \(A\setminus B\) consists of all elements of \(A\) except those that are also in \(B\). The elements removed from \(A\) are precisely the elements in \(A\cap B\). Therefore, subtracting the size of the common part from the size of \(A\) gives \(n(A\setminus B)=n(A)-n(A\cap B)\). Option C is numerically equivalent, because \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\), but the requested direct formula is option A.
Frequently asked questions
What is the correct answer to this question?
\(n(A)-n(A\cap B)\)
Why is this the correct answer?
The set \(A\setminus B\) consists of all elements of \(A\) except those that are also in \(B\). The elements removed from \(A\) are precisely the elements in \(A\cap B\). Therefore, subtracting the size of the common part from the size of \(A\) gives \(n(A\setminus B)=n(A)-n(A\cap B)\). Option C is numerically equivalent, because \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\), but the requested direct formula is option A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
