If n(A ∩ B') = 24, n(A' ∩ B) = 31, and n(A ∩ B) = 16, what is n(A ∪ B)?
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Answer and explanation
Correct answer: 71
The union A ∪ B is divided into three mutually disjoint Venn regions: A only, represented by A ∩ B' and equal to 24; B only, represented by A' ∩ B and equal to 31; and the common region A ∩ B, equal to 16. Adding these non-overlapping parts gives 24 + 31 + 16 = 71. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
71
Why is this the correct answer?
The union A ∪ B is divided into three mutually disjoint Venn regions: A only, represented by A ∩ B' and equal to 24; B only, represented by A' ∩ B and equal to 31; and the common region A ∩ B, equal to 16. Adding these non-overlapping parts gives 24 + 31 + 16 = 71. Therefore, 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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