In three sets, n(A ∩ B) = 36, n(B ∩ C) = 33, n(C ∩ A) = 31, and n(A ∩ B ∩ C) = 14. How many elements belong to exactly two sets?
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Answer and explanation
Correct answer: 58
Each pairwise intersection includes the elements that lie in all three sets. Thus, the elements in exactly A and B are 36 − 14 = 22; exactly B and C are 33 − 14 = 19; and exactly C and A are 31 − 14 = 17. Adding these disjoint regions gives 22 + 19 + 17 = 58. Therefore option B is correct.
Frequently asked questions
What is the correct answer to this question?
58
Why is this the correct answer?
Each pairwise intersection includes the elements that lie in all three sets. Thus, the elements in exactly A and B are 36 − 14 = 22; exactly B and C are 33 − 14 = 19; and exactly C and A are 31 − 14 = 17. Adding these disjoint regions gives 22 + 19 + 17 = 58. Therefore option B 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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