In a three-set Venn diagram, \(n(A\cap B)=12\), \(n(B\cap C)=13\), \(n(C\cap A)=10\), and \(n(A\cap B\cap C)=4\). How many elements lie in exactly two of the sets?
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Answer and explanation
Correct answer: 23
Each pairwise intersection includes the central three-set intersection, so subtract 4 from each pair to obtain the pair-only regions. For A and B, the count is \(12-4=8\); for B and C, it is \(13-4=9\); and for C and A, it is \(10-4=6\). Therefore, exactly two sets contain \(8+9+6=23\) elements. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
23
Why is this the correct answer?
Each pairwise intersection includes the central three-set intersection, so subtract 4 from each pair to obtain the pair-only regions. For A and B, the count is \(12-4=8\); for B and C, it is \(13-4=9\); and for C and A, it is \(10-4=6\). Therefore, exactly two sets contain \(8+9+6=23\) elements. 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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