If n(A∪B)=112, n(A−B)=43, and n(B−A)=37, what is n(A∩B)?
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Answer and explanation
Correct answer: 32
In a two-set Venn diagram, A ∪ B consists of three non-overlapping regions: A − B, B − A, and A ∩ B. Therefore n(A ∪ B) = n(A − B) + n(B − A) + n(A ∩ B). Substituting gives 112 = 43 + 37 + n(A ∩ B). Since 43 + 37 = 80, the intersection has 112 − 80 = 32 elements. Thus option A is the unique correct answer.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
In a two-set Venn diagram, A ∪ B consists of three non-overlapping regions: A − B, B − A, and A ∩ B. Therefore n(A ∪ B) = n(A − B) + n(B − A) + n(A ∩ B). Substituting gives 112 = 43 + 37 + n(A ∩ B). Since 43 + 37 = 80, the intersection has 112 − 80 = 32 elements. Thus option A is the unique correct answer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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