If \(n(A)=28\), \(n(B)=19\), and \(n(A\cup B)=39\), what is \(n(A\cap B)\)?
Answer and explanation
Correct answer: 8
For two finite sets, the inclusion–exclusion formula is \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\). Therefore, \(n(A\cap B)=28+19-39=8\). The intersection is subtracted because common elements are counted once in \(n(A)\) and again in \(n(B)\). Thus, option B is correct; 11 results from an arithmetic or formula error.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
For two finite sets, the inclusion–exclusion formula is \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\). Therefore, \(n(A\cap B)=28+19-39=8\). The intersection is subtracted because common elements are counted once in \(n(A)\) and again in \(n(B)\). Thus, option B is correct; 11 results from an arithmetic or formula error.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
