In a Venn diagram, n(A △ B) = 82 and n(A ∪ B) = 119. What is n(A ∩ B)?
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Answer and explanation
Correct answer: 37
The union A ∪ B is made up of two disjoint parts: the symmetric difference A △ B, containing elements in exactly one of the sets, and the intersection A ∩ B, containing elements common to both sets. Therefore, n(A ∪ B) = n(A △ B) + n(A ∩ B). Thus, n(A ∩ B) = 119 − 82 = 37, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
37
Why is this the correct answer?
The union A ∪ B is made up of two disjoint parts: the symmetric difference A △ B, containing elements in exactly one of the sets, and the intersection A ∩ B, containing elements common to both sets. Therefore, n(A ∪ B) = n(A △ B) + n(A ∩ B). Thus, n(A ∩ B) = 119 − 82 = 37, so 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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