If n(A − B) = x, n(B − A) = 2x, n(A ∩ B) = 15, and n(A ∪ B) = 75, what is the value of x?
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Answer and explanation
Correct answer: 20
The union A ∪ B consists of three mutually disjoint regions: the elements only in A, the elements only in B, and the elements common to both sets. Therefore, n(A ∪ B) = n(A − B) + n(B − A) + n(A ∩ B). Substituting the given values gives 75 = x + 2x + 15, so 3x = 60 and x = 20. Hence, option B is correct.
Frequently asked questions
What is the correct answer to this question?
20
Why is this the correct answer?
The union A ∪ B consists of three mutually disjoint regions: the elements only in A, the elements only in B, and the elements common to both sets. Therefore, n(A ∪ B) = n(A − B) + n(B − A) + n(A ∩ B). Substituting the given values gives 75 = x + 2x + 15, so 3x = 60 and x = 20. Hence, option B 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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