If n(A) = 26, n(B) = 18, and n(A ∩ B) = 8, what is n(A ∪ B)?
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Answer and explanation
Correct answer: 36
For two finite sets, the inclusion–exclusion principle gives n(A ∪ B) = n(A) + n(B) − n(A ∩ B). The subtraction is necessary because the 8 elements common to A and B are counted once in n(A) and once in n(B). Thus n(A ∪ B) = 26 + 18 − 8 = 36. Therefore, option A is correct; 44 results from forgetting the overlap.
Frequently asked questions
What is the correct answer to this question?
36
Why is this the correct answer?
For two finite sets, the inclusion–exclusion principle gives n(A ∪ B) = n(A) + n(B) − n(A ∩ B). The subtraction is necessary because the 8 elements common to A and B are counted once in n(A) and once in n(B). Thus n(A ∪ B) = 26 + 18 − 8 = 36. Therefore, option A is correct; 44 results from forgetting the overlap.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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