If A ∩ B = ∅, n(A) = 26, and n(B) = 19, what is n(A ∪ B)?
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Answer and explanation
Correct answer: 45
The condition A ∩ B = ∅ means that A and B are disjoint sets; they have no common elements. For any two sets, n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Here the intersection has cardinality zero, so n(A ∪ B) = 26 + 19 − 0 = 45. Thus all elements from both sets are counted exactly once.
Frequently asked questions
What is the correct answer to this question?
45
Why is this the correct answer?
The condition A ∩ B = ∅ means that A and B are disjoint sets; they have no common elements. For any two sets, n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Here the intersection has cardinality zero, so n(A ∪ B) = 26 + 19 − 0 = 45. Thus all elements from both sets are counted exactly once.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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