If n(A − B) = x, n(B − A) = 3x, n(A ∩ B) = 24, and n(A ∪ B) = 120, what is x?
Answer and explanation
Correct answer: 24
The union of two sets is divided into three disjoint Venn-diagram regions: A − B, B − A, and A ∩ B. Therefore n(A ∪ B) = n(A − B) + n(B − A) + n(A ∩ B). Substituting the given expressions gives 120 = x + 3x + 24. Thus 4x = 96 and x = 24. Consequently, n(A − B) is 24 and n(B − A) is 72, whose total with the intersection is 120.
Frequently asked questions
What is the correct answer to this question?
24
Why is this the correct answer?
The union of two sets is divided into three disjoint Venn-diagram regions: A − B, B − A, and A ∩ B. Therefore n(A ∪ B) = n(A − B) + n(B − A) + n(A ∩ B). Substituting the given expressions gives 120 = x + 3x + 24. Thus 4x = 96 and x = 24. Consequently, n(A − B) is 24 and n(B − A) is 72, whose total with the intersection is 120.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
