If n(A) = 35, n(B) = 27, and n(A ∪ B) = 50, what is n(A ∩ B)?
Answer and explanation
Correct answer: 12
Use the two-set cardinality formula n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Rearranging gives n(A ∩ B) = n(A) + n(B) − n(A ∪ B). Substituting the values gives 35 + 27 − 50 = 12. Thus, twelve elements belong to both A and B, so option A is correct. The result is reasonable because the union is smaller than 35 + 27 due to overlap.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
Use the two-set cardinality formula n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Rearranging gives n(A ∩ B) = n(A) + n(B) − n(A ∪ B). Substituting the values gives 35 + 27 − 50 = 12. Thus, twelve elements belong to both A and B, so option A is correct. The result is reasonable because the union is smaller than 35 + 27 due to overlap.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
