If n(A \ B) = 12, n(B \ A) = 9, and n(A ∩ B) = 6, what is the value of n(A ∪ B)?
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Answer and explanation
Correct answer: 27
The sets A and B can be divided into three non-overlapping regions: elements only in A, elements only in B, and elements in both sets. Their sizes are 12, 9, and 6 respectively. The union contains all three regions, so n(A ∪ B) = 12 + 9 + 6 = 27. Thus, option A is correct.
Frequently asked questions
What is the correct answer to this question?
27
Why is this the correct answer?
The sets A and B can be divided into three non-overlapping regions: elements only in A, elements only in B, and elements in both sets. Their sizes are 12, 9, and 6 respectively. The union contains all three regions, so n(A ∪ B) = 12 + 9 + 6 = 27. Thus, 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).
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