In a Venn diagram, n(A ∩ B) = 0 and n(A ∪ B) = 76. If n(A) = 31, what is n(B)?
Answer and explanation
Correct answer: 45
Use the cardinality formula n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the given values gives 76 = 31 + n(B) − 0. Therefore, n(B) = 76 − 31 = 45. The zero intersection means that A and B are disjoint, so no common elements are counted twice. Option A is n(A), option C is the union, and option D incorrectly adds 31 and 76.
Frequently asked questions
What is the correct answer to this question?
45
Why is this the correct answer?
Use the cardinality formula n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the given values gives 76 = 31 + n(B) − 0. Therefore, n(B) = 76 − 31 = 45. The zero intersection means that A and B are disjoint, so no common elements are counted twice. Option A is n(A), option C is the union, and option D incorrectly adds 31 and 76.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
