In a Venn diagram, n(A ∪ B) = 70, n(A − B) = 24, and n(B − A) = 31. What is n(A ∩ B)?
Answer and explanation
Correct answer: 15
For two sets, the union consists of three non-overlapping regions: the elements only in A, represented by A − B; the elements only in B, represented by B − A; and the common elements, represented by A ∩ B. Hence n(A ∪ B) = n(A − B) + n(B − A) + n(A ∩ B). Substituting the values gives 70 = 24 + 31 + n(A ∩ B), so n(A ∩ B) = 15. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
For two sets, the union consists of three non-overlapping regions: the elements only in A, represented by A − B; the elements only in B, represented by B − A; and the common elements, represented by A ∩ B. Hence n(A ∪ B) = n(A − B) + n(B − A) + n(A ∩ B). Substituting the values gives 70 = 24 + 31 + n(A ∩ B), so n(A ∩ B) = 15. Option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
