If A ∩ B = ∅, n(A) = 33, and n(B) = 41, what is n(A ∪ B)?
Answer and explanation
Correct answer: 74
The governing concept is the cardinality formula for the union of two finite sets: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Since A ∩ B = ∅, the sets are disjoint and their intersection has zero elements. Therefore, n(A ∪ B) = 33 + 41 − 0 = 74. Options C and D give the size of only one set, while option B is the difference, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
74
Why is this the correct answer?
The governing concept is the cardinality formula for the union of two finite sets: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Since A ∩ B = ∅, the sets are disjoint and their intersection has zero elements. Therefore, n(A ∪ B) = 33 + 41 − 0 = 74. Options C and D give the size of only one set, while option B is the difference, so 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).
