If n(A − B) = x + 4, n(B − A) = 2x − 1, n(A ∩ B) = x + 3, and n(A ∪ B) = 46, what is the value of x?
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Answer and explanation
Correct answer: 10
The union is divided into three disjoint parts: A − B, B − A, and A ∩ B. Hence n(A ∪ B) = (x + 4) + (2x − 1) + (x + 3). Substituting 46 gives 4x + 6 = 46, so 4x = 40 and x = 10. The corresponding regions are 14, 19, and 13, and 14 + 19 + 13 = 46, confirming the result. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
The union is divided into three disjoint parts: A − B, B − A, and A ∩ B. Hence n(A ∪ B) = (x + 4) + (2x − 1) + (x + 3). Substituting 46 gives 4x + 6 = 46, so 4x = 40 and x = 10. The corresponding regions are 14, 19, and 13, and 14 + 19 + 13 = 46, confirming the result. Therefore option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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