If n(A ∪ B) = 74, n(A − B) = 28, and n(B − A) = 19, what is n(A ∩ B)?
Answer and explanation
Correct answer: 27
A union B consists of three mutually exclusive regions in a Venn diagram: the elements only in A, the elements common to both A and B, and the elements only in B. Therefore, n(A ∪ B) = n(A − B) + n(A ∩ B) + n(B − A). Substituting the values gives 74 = 28 + n(A ∩ B) + 19, so n(A ∩ B) = 74 − 28 − 19 = 27. Hence, option C is correct.
Frequently asked questions
What is the correct answer to this question?
27
Why is this the correct answer?
A union B consists of three mutually exclusive regions in a Venn diagram: the elements only in A, the elements common to both A and B, and the elements only in B. Therefore, n(A ∪ B) = n(A − B) + n(A ∩ B) + n(B − A). Substituting the values gives 74 = 28 + n(A ∩ B) + 19, so n(A ∩ B) = 74 − 28 − 19 = 27. Hence, option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
