If \(n(A\cup B)=75\), \(n(A-B)=28\), and \(n(B-A)=31\), what is \(n(A\cap B)\)?
Answer and explanation
Correct answer: 16
The union \(A\cup B\) is partitioned into three mutually disjoint parts: \(A-B\), \(B-A\), and \(A\cap B\). Let \(n(A\cap B)=x\). Then \(75=28+31+x\). Hence \(x=75-59=16\). Therefore, the intersection contains 16 elements. The calculation also shows why the difference parts must not be counted as overlapping with each other.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
The union \(A\cup B\) is partitioned into three mutually disjoint parts: \(A-B\), \(B-A\), and \(A\cap B\). Let \(n(A\cap B)=x\). Then \(75=28+31+x\). Hence \(x=75-59=16\). Therefore, the intersection contains 16 elements. The calculation also shows why the difference parts must not be counted as overlapping with each other.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
