If n(A ∪ B) = 104, n(A ∩ B) = 26, and n(A − B) = 37, what is n(B)?
Answer and explanation
Correct answer: 67
The union is partitioned into the disjoint regions \(A-B\), \(A\cap B\), and \(B-A\). Hence \(n(B-A)=104-37-26=41\). Set \(B\) consists of the region \(B-A\) together with the intersection, so \(n(B)=41+26=67\). Thus option C is correct. Option A is only the size of \(B-A\), while the other values do not follow from the partition.
Frequently asked questions
What is the correct answer to this question?
67
Why is this the correct answer?
The union is partitioned into the disjoint regions \(A-B\), \(A\cap B\), and \(B-A\). Hence \(n(B-A)=104-37-26=41\). Set \(B\) consists of the region \(B-A\) together with the intersection, so \(n(B)=41+26=67\). Thus option C is correct. Option A is only the size of \(B-A\), while the other values do not follow from the partition.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
