If n(A − B) = 2x + 3, n(B − A) = x + 7, n(A ∩ B) = x − 1, and n(A ∪ B) = 45, what is the value of x?
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Answer and explanation
Correct answer: 9
The union A ∪ B is partitioned into three disjoint regions: A − B, B − A and A ∩ B. Therefore, 45 = (2x+3) + (x+7) + (x−1) = 4x+9. Subtracting 9 gives 4x = 36, and dividing by 4 gives x = 9. Option A is correct. The other values do not satisfy the stated union equation.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
The union A ∪ B is partitioned into three disjoint regions: A − B, B − A and A ∩ B. Therefore, 45 = (2x+3) + (x+7) + (x−1) = 4x+9. Subtracting 9 gives 4x = 36, and dividing by 4 gives x = 9. Option A is correct. The other values do not satisfy the stated union equation.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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