If \(n(U)=85\) and \(n(A\cup B)=56\), how many elements are in neither \(A\) nor \(B\)?
Answer and explanation
Correct answer: 29
The union \(A\cup B\) contains every element that belongs to at least one of the two sets. The elements in neither set are outside this union but still inside the universal set. Hence their number is \(n(U)-n(A\cup B)=85-56=29\). Therefore, option A is correct. The value 56 counts the union itself, not the region outside both sets.
Frequently asked questions
What is the correct answer to this question?
29
Why is this the correct answer?
The union \(A\cup B\) contains every element that belongs to at least one of the two sets. The elements in neither set are outside this union but still inside the universal set. Hence their number is \(n(U)-n(A\cup B)=85-56=29\). Therefore, option A is correct. The value 56 counts the union itself, not the region outside both sets.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
