If two sets A and B are disjoint, where n(A) = 15 and n(B) = 19, what is n(A ∪ B)?
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Answer and explanation
Correct answer: 34
Disjoint sets have no common elements, so A ∩ B = ∅ and n(A ∩ B) = 0. The general formula is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the given values gives n(A ∪ B) = 15 + 19 − 0 = 34. Thus every element from both sets is counted exactly once in the union.
Frequently asked questions
What is the correct answer to this question?
34
Why is this the correct answer?
Disjoint sets have no common elements, so A ∩ B = ∅ and n(A ∩ B) = 0. The general formula is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the given values gives n(A ∪ B) = 15 + 19 − 0 = 34. Thus every element from both sets is counted exactly once in the union.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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