If n(A) = 69, n(B) = 74, and n(A − B) = 28, what is n(A ∪ B)?
Answer and explanation
Correct answer: 102
The set A is the disjoint union of A − B and A ∩ B. Thus n(A ∩ B) = n(A) − n(A − B) = 69 − 28 = 41. Now apply the union formula: n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 69 + 74 − 41 = 102. The value 143 incorrectly counts the common elements twice, while 41 is only the intersection. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
102
Why is this the correct answer?
The set A is the disjoint union of A − B and A ∩ B. Thus n(A ∩ B) = n(A) − n(A − B) = 69 − 28 = 41. Now apply the union formula: n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 69 + 74 − 41 = 102. The value 143 incorrectly counts the common elements twice, while 41 is only the intersection. Therefore option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
