If n(A) = 6x + 5, n(B) = 5x + 9, n(A ∩ B) = 3x + 4 and n(A ∪ B) = 106, then what is the value of x?
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Answer and explanation
Correct answer: 12
Apply the two-set union formula: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substitution gives 106 = (6x + 5) + (5x + 9) − (3x + 4). Simplifying, 106 = 8x + 10, so 8x = 96 and x = 12. Substitution confirms that the three cardinalities are 77, 69, and 40, whose union is 106.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
Apply the two-set union formula: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substitution gives 106 = (6x + 5) + (5x + 9) − (3x + 4). Simplifying, 106 = 8x + 10, so 8x = 96 and x = 12. Substitution confirms that the three cardinalities are 77, 69, and 40, whose union is 106.
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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