For three activities, n(A) = 84, n(B) = 77, n(C) = 73, n(A ∩ B) = 33, n(B ∩ C) = 28, n(C ∩ A) = 31 and n(A ∩ B ∩ C) = 13. How many students are only in A ∩ C, that is, in A and C but not in B?
Answer and explanation
Correct answer: 18
The number n(A ∩ C) = 31 includes every student who belongs to both A and C, including those who also belong to B. The triple intersection has 13 students, so these must be removed to obtain the pair-only region. Hence the number in A ∩ C but not B is 31 − 13 = 18. The value 31 would incorrectly include the triple intersection.
Frequently asked questions
What is the correct answer to this question?
18
Why is this the correct answer?
The number n(A ∩ C) = 31 includes every student who belongs to both A and C, including those who also belong to B. The triple intersection has 13 students, so these must be removed to obtain the pair-only region. Hence the number in A ∩ C but not B is 31 − 13 = 18. The value 31 would incorrectly include the triple intersection.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
