If \(n(U)=52\) and \(n(A\cup B)=37\), how many elements are in neither \(A\) nor \(B\)?
Answer and explanation
Correct answer: 15
The elements in neither A nor B are the elements in the universal set that lie outside the union \(A\cup B\). Therefore, this region is the complement of the union, \((A\cup B)'\), and its cardinality is \(n(U)-n(A\cup B)=52-37=15\). Thus, option A is correct. The value 37 counts the union itself, 52 counts the entire universal set, and 89 incorrectly adds the two given numbers.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
The elements in neither A nor B are the elements in the universal set that lie outside the union \(A\cup B\). Therefore, this region is the complement of the union, \((A\cup B)'\), and its cardinality is \(n(U)-n(A\cup B)=52-37=15\). Thus, option A is correct. The value 37 counts the union itself, 52 counts the entire universal set, and 89 incorrectly adds the two given numbers.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
