If \(n(A)=18\) and \(n(A\cap B)=6\), how many elements are only in \(A\)?
Answer and explanation
Correct answer: 12
The set \(A\) is divided into two non-overlapping parts: the elements only in \(A\), represented by \(A-B\), and the common elements \(A\cap B\). Therefore, \(n(A)=n(A-B)+n(A\cap B)\). Rearranging gives \(n(A-B)=18-6=12\). Thus, option B is correct. The value 6 is only the overlap, while 18 includes both parts.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
The set \(A\) is divided into two non-overlapping parts: the elements only in \(A\), represented by \(A-B\), and the common elements \(A\cap B\). Therefore, \(n(A)=n(A-B)+n(A\cap B)\). Rearranging gives \(n(A-B)=18-6=12\). Thus, option B is correct. The value 6 is only the overlap, while 18 includes both parts.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
