If n(A ∪ B) = 44, the number of elements only in A is 16, and the number of elements only in B is 19, what is n(A ∩ B)?
Answer and explanation
Correct answer: 9
The union consists of three disjoint Venn-diagram regions: elements only in A, elements common to A and B, and elements only in B. Thus, 44 = 16 + n(A ∩ B) + 19. Subtracting the two exclusive regions gives n(A ∩ B) = 44 − 16 − 19 = 9. Hence, option A is correct. Options B and C are the given exclusive counts, while 35 is their combined total.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
The union consists of three disjoint Venn-diagram regions: elements only in A, elements common to A and B, and elements only in B. Thus, 44 = 16 + n(A ∩ B) + 19. Subtracting the two exclusive regions gives n(A ∩ B) = 44 − 16 − 19 = 9. Hence, option A is correct. Options B and C are the given exclusive counts, while 35 is their combined total.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
