If only A = 25, only A ∩ B = 14, only A ∩ C = 12, and A ∩ B ∩ C = 9, what is n(A)?
Answer and explanation
Correct answer: 60
A consists of every Venn-diagram region lying inside circle A. These are the part only in A, the part only in A ∩ B, the part only in A ∩ C, and the central part in all three sets. Therefore n(A) = 25 + 14 + 12 + 9 = 60. The pairwise values are explicitly labelled “only,” so they must not be counted again in any other way. Option B is correct.
Frequently asked questions
What is the correct answer to this question?
60
Why is this the correct answer?
A consists of every Venn-diagram region lying inside circle A. These are the part only in A, the part only in A ∩ B, the part only in A ∩ C, and the central part in all three sets. Therefore n(A) = 25 + 14 + 12 + 9 = 60. The pairwise values are explicitly labelled “only,” so they must not be counted again in any other way. Option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
