If \(n(A\cup B)=72\), \(n(A)=46\), and \(n(B-A)=26\), what is \(n(A\cap B)\)?
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Answer and explanation
Correct answer: 0
The set B can be divided into two disjoint regions: the common part \(A\cap B\) and the B-only part \(B-A\). Also, the union consists of A together with the B-only part, so \(n(A\cup B)=n(A)+n(B-A)=46+26=72\). Since this already equals the given union, no additional common part is present; therefore \(n(A\cap B)=0\).
Frequently asked questions
What is the correct answer to this question?
0
Why is this the correct answer?
The set B can be divided into two disjoint regions: the common part \(A\cap B\) and the B-only part \(B-A\). Also, the union consists of A together with the B-only part, so \(n(A\cup B)=n(A)+n(B-A)=46+26=72\). Since this already equals the given union, no additional common part is present; therefore \(n(A\cap B)=0\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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