If n(A union B) = 70, n(A − B) = 26, and n(B − A) = 19, what is n(A intersection B)?
Answer and explanation
Correct answer: 25
A union B is partitioned into exactly three mutually disjoint regions: the A-only region A − B, the common region A intersection B, and the B-only region B − A. Therefore, n(A union B) = n(A − B) + n(A intersection B) + n(B − A). Substituting the values gives 70 = 26 + n(A intersection B) + 19. Hence n(A intersection B) = 70 − 26 − 19 = 25. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
25
Why is this the correct answer?
A union B is partitioned into exactly three mutually disjoint regions: the A-only region A − B, the common region A intersection B, and the B-only region B − A. Therefore, n(A union B) = n(A − B) + n(A intersection B) + n(B − A). Substituting the values gives 70 = 26 + n(A intersection B) + 19. Hence n(A intersection B) = 70 − 26 − 19 = 25. Option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
