In a Venn diagram, n(A − B) = 25, n(B − A) = 30, n(A ∩ B) = 20, and n((A ∪ B)ᶜ) = 15. What is n(Aᶜ)?
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Answer and explanation
Correct answer: 45
The complement \(A^c\) contains all elements outside \(A\). In the Venn diagram, these are exactly the region \(B-A\) and the region outside \(A\cup B\). The intersection lies inside \(A\), so it must not be counted. Therefore \(n(A^c)=n(B-A)+n((A\cup B)^c)=30+15=45\). Option A is correct.
Frequently asked questions
What is the correct answer to this question?
45
Why is this the correct answer?
The complement \(A^c\) contains all elements outside \(A\). In the Venn diagram, these are exactly the region \(B-A\) and the region outside \(A\cup B\). The intersection lies inside \(A\), so it must not be counted. Therefore \(n(A^c)=n(B-A)+n((A\cup B)^c)=30+15=45\). Option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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