If n(A − B) = x + 5, n(B − A) = 2x − 3, n(A ∩ B) = x + 1, and n(A ∪ B) = 43, what is the value of x?
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Answer and explanation
Correct answer: 10
The three regions A − B, B − A, and A ∩ B are mutually disjoint, and together they form A ∪ B. Therefore, (x + 5) + (2x − 3) + (x + 1) = 43. Simplifying gives 4x + 3 = 43, so 4x = 40 and x = 10. The three region sizes are then 15, 17, and 11, whose sum is 43. Thus option A is the only correct answer.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
The three regions A − B, B − A, and A ∩ B are mutually disjoint, and together they form A ∪ B. Therefore, (x + 5) + (2x − 3) + (x + 1) = 43. Simplifying gives 4x + 3 = 43, so 4x = 40 and x = 10. The three region sizes are then 15, 17, and 11, whose sum is 43. Thus option A is the only 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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