If n(A) = 86, n(B) = 79, n(C) = 71, n(A ∩ B) = 34, n(B ∩ C) = 29, n(C ∩ A) = 27, and n(A ∩ B ∩ C) = 12, then how many elements are only in C?
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Answer and explanation
Correct answer: 27
The elements only in C are those in C but not in A or B. Start with n(C) = 71. Subtract n(B ∩ C) = 29 and n(C ∩ A) = 27, because these are the portions of C shared with the other sets. The central region A ∩ B ∩ C, containing 12 elements, was subtracted twice, so add it back once. Thus only-C = 71 − 29 − 27 + 12 = 27.
Frequently asked questions
What is the correct answer to this question?
27
Why is this the correct answer?
The elements only in C are those in C but not in A or B. Start with n(C) = 71. Subtract n(B ∩ C) = 29 and n(C ∩ A) = 27, because these are the portions of C shared with the other sets. The central region A ∩ B ∩ C, containing 12 elements, was subtracted twice, so add it back once. Thus only-C = 71 − 29 − 27 + 12 = 27.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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