In a two-set Venn diagram, n(A − B) = 26, n(A ∩ B) = 18, n(B − A) = 33, and 12 elements are outside both sets. What is n(U)?
Answer and explanation
Correct answer: 89
The universal set contains every region shown in the Venn diagram. These regions are the A-only region A − B, the common region A ∩ B, the B-only region B − A, and the region outside both sets. Therefore, n(U) = 26 + 18 + 33 + 12 = 89. Since the regions are disjoint and together cover U, no subtraction or overlap correction is needed.
Frequently asked questions
What is the correct answer to this question?
89
Why is this the correct answer?
The universal set contains every region shown in the Venn diagram. These regions are the A-only region A − B, the common region A ∩ B, the B-only region B − A, and the region outside both sets. Therefore, n(U) = 26 + 18 + 33 + 12 = 89. Since the regions are disjoint and together cover U, no subtraction or overlap correction is needed.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
