If only \(A\) has 18 elements, \(A\cap B\) has 7 elements, and only \(B\) has 14 elements, what is \(n(A\cup B)\)?
Answer and explanation
Correct answer: 39
The union contains every element in at least one of the sets. Its three disjoint Venn-diagram regions are only A, the intersection, and only B. Therefore, \(n(A\cup B)=18+7+14=39\). Each element is counted exactly once because the regions are disjoint. Hence option C is correct; adding only the two exclusive regions would incorrectly omit the seven common elements.
Frequently asked questions
What is the correct answer to this question?
39
Why is this the correct answer?
The union contains every element in at least one of the sets. Its three disjoint Venn-diagram regions are only A, the intersection, and only B. Therefore, \(n(A\cup B)=18+7+14=39\). Each element is counted exactly once because the regions are disjoint. Hence option C is correct; adding only the two exclusive regions would incorrectly omit the seven common elements.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
