If n(A ∩ B′) = 29, n(A′ ∩ B) = 34, and n(A ∩ B) = 21, what is n(A ∪ B)?
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Answer and explanation
Correct answer: 84
The union A ∪ B is partitioned into three mutually exclusive regions: A ∩ B′, A′ ∩ B, and A ∩ B. The outside region A′ ∩ B′ is not part of the union. Therefore n(A ∪ B) = 29 + 34 + 21 = 84. Option A is correct; subtracting or omitting one region produces the distractor values.
Frequently asked questions
What is the correct answer to this question?
84
Why is this the correct answer?
The union A ∪ B is partitioned into three mutually exclusive regions: A ∩ B′, A′ ∩ B, and A ∩ B. The outside region A′ ∩ B′ is not part of the union. Therefore n(A ∪ B) = 29 + 34 + 21 = 84. Option A is correct; subtracting or omitting one region produces the distractor values.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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