If \(n(U)=94\), there are 26 elements only in \(A\), 15 elements in \(A\cap B\), and 31 elements only in \(B\), how many elements lie in neither \(A\) nor \(B\)?
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Answer and explanation
Correct answer: 22
The three listed regions inside \(A\cup B\) are disjoint, so their total is \(26+15+31=72\). The universal set has 94 elements, and the remaining elements are outside both sets. Hence, the number in neither set is \(94-72=22\). Option A is correct; 72 is the union count, not the outside count.
Frequently asked questions
What is the correct answer to this question?
22
Why is this the correct answer?
The three listed regions inside \(A\cup B\) are disjoint, so their total is \(26+15+31=72\). The universal set has 94 elements, and the remaining elements are outside both sets. Hence, the number in neither set is \(94-72=22\). Option A is correct; 72 is the union count, not the outside count.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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