If \(n(A)=23\) and \(n(A\cap B)=9\), how many elements belong only to \(A\)?
Answer and explanation
Correct answer: 14
The set A consists of two disjoint parts: the elements only in A and the elements shared by A and B. Hence, \(n(A)=n(A\text{ only})+n(A\cap B)\). Therefore, the number only in A is \(23-9=14\). Option B is correct. The value 9 counts only the common region, 23 counts all elements of A including the common region, and 32 results from adding instead of subtracting the shared elements.
Frequently asked questions
What is the correct answer to this question?
14
Why is this the correct answer?
The set A consists of two disjoint parts: the elements only in A and the elements shared by A and B. Hence, \(n(A)=n(A\text{ only})+n(A\cap B)\). Therefore, the number only in A is \(23-9=14\). Option B is correct. The value 9 counts only the common region, 23 counts all elements of A including the common region, and 32 results from adding instead of subtracting the shared 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).
