If \(n(A-B)=6\), \(n(A\cap B)=5\), and \(n(B-A)=4\), what is \(n(A\cup B)\)?
Answer and explanation
Correct answer: 15
The union \(A\cup B\) contains every element that is in \(A\), in \(B\), or in both. Its Venn diagram has exactly three disjoint regions: only \(A\), the overlap \(A\cap B\), and only \(B\). Therefore, \(n(A\cup B)=6+5+4=15\). Option C is correct. Adding only the exclusive regions would omit the overlap, while counting totals separately could double-count it.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
The union \(A\cup B\) contains every element that is in \(A\), in \(B\), or in both. Its Venn diagram has exactly three disjoint regions: only \(A\), the overlap \(A\cap B\), and only \(B\). Therefore, \(n(A\cup B)=6+5+4=15\). Option C is correct. Adding only the exclusive regions would omit the overlap, while counting totals separately could double-count it.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
