If n(A − B) = 4x + 1, n(B − A) = 3x + 6, n(A ∩ B) = 2x + 5 and n(A ∪ B) = 120, then what is x?
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Answer and explanation
Correct answer: 12
The union is partitioned into three mutually disjoint regions: A − B, B − A, and A ∩ B. Therefore their cardinalities add directly: (4x + 1) + (3x + 6) + (2x + 5) = 120. This simplifies to 9x + 12 = 120, so 9x = 108 and x = 12. At x = 12, the three regions are 49, 42, and 29, which sum to 120.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
The union is partitioned into three mutually disjoint regions: A − B, B − A, and A ∩ B. Therefore their cardinalities add directly: (4x + 1) + (3x + 6) + (2x + 5) = 120. This simplifies to 9x + 12 = 120, so 9x = 108 and x = 12. At x = 12, the three regions are 49, 42, and 29, which sum to 120.
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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