If n(A ∪ B) = 96, n(A) = 58, and n(A − B) = 29, what is n(B − A)?
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Answer and explanation
Correct answer: 38
First separate set A into its exclusive and common parts: n(A) = n(A−B)+n(A∩B). Therefore n(A∩B) = 58−29 = 29. The union then contains A−B, A∩B, and B−A as disjoint regions. Hence 96 = 29+29+n(B−A), giving n(B−A) = 38. Equivalently, n(B−A)=n(A∪B)−n(A)=96−58=38. Thus option A is correct.
Frequently asked questions
What is the correct answer to this question?
38
Why is this the correct answer?
First separate set A into its exclusive and common parts: n(A) = n(A−B)+n(A∩B). Therefore n(A∩B) = 58−29 = 29. The union then contains A−B, A∩B, and B−A as disjoint regions. Hence 96 = 29+29+n(B−A), giving n(B−A) = 38. Equivalently, n(B−A)=n(A∪B)−n(A)=96−58=38. Thus 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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