If \(n(B)=14\) and \(n(A\cap B)=5\), how many elements are only in \(B\)?
Answer and explanation
Correct answer: 9
The elements of \(B\) consist of the elements only in \(B\) together with the common elements in \(A\cap B\). Hence, \(n(B)=n(B-A)+n(A\cap B)\). Substituting the given values gives \(n(B-A)=14-5=9\). Therefore, option B is correct. The value 5 counts the overlap, and 14 counts all of \(B\), not only its exclusive region.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
The elements of \(B\) consist of the elements only in \(B\) together with the common elements in \(A\cap B\). Hence, \(n(B)=n(B-A)+n(A\cap B)\). Substituting the given values gives \(n(B-A)=14-5=9\). Therefore, option B is correct. The value 5 counts the overlap, and 14 counts all of \(B\), not only its exclusive region.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
