In a Venn diagram of two sets, n(A − B) = 12, n(B − A) = 9, and n(A ∩ B) = 6. What is n(A ∪ B)?
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Answer and explanation
Correct answer: 27
The union of two sets is partitioned into three non-overlapping regions: A − B, A ∩ B, and B − A. Therefore, n(A ∪ B) = n(A − B) + n(A ∩ B) + n(B − A) = 12 + 6 + 9 = 27. Since these regions do not overlap, their sizes can be added directly. Hence, option A is correct.
Frequently asked questions
What is the correct answer to this question?
27
Why is this the correct answer?
The union of two sets is partitioned into three non-overlapping regions: A − B, A ∩ B, and B − A. Therefore, n(A ∪ B) = n(A − B) + n(A ∩ B) + n(B − A) = 12 + 6 + 9 = 27. Since these regions do not overlap, their sizes can be added directly. Hence, option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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