If \(n(U)=76\), 18 elements lie outside \(A\cup B\), only \(A\) has 20 elements, and only \(B\) has 23 elements, what is \(n(A\cap B)\)?
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Answer and explanation
Correct answer: 15
The universal set is divided into four disjoint regions: only A, the intersection, only B, and neither set. Their total is 76. Therefore, \(n(A\cap B)=76-(20+23+18)=76-61=15\). Option A is correct. The value 61 is only the sum of the three known regions, so it excludes the unknown intersection rather than representing it.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
The universal set is divided into four disjoint regions: only A, the intersection, only B, and neither set. Their total is 76. Therefore, \(n(A\cap B)=76-(20+23+18)=76-61=15\). Option A is correct. The value 61 is only the sum of the three known regions, so it excludes the unknown intersection rather than representing it.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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