If n(A) = 5x + 4, n(B) = 4x + 7, n(A ∩ B) = 2x + 3, and n(A ∪ B) = 78, what is the value of x?
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Answer and explanation
Correct answer: 10
Apply the inclusion–exclusion formula for two finite sets: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the given expressions gives 78 = (5x + 4) + (4x + 7) − (2x + 3). Simplifying, 78 = 7x + 8, so 7x = 70 and x = 10. Substitution confirms the result, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
Apply the inclusion–exclusion formula for two finite sets: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the given expressions gives 78 = (5x + 4) + (4x + 7) − (2x + 3). Simplifying, 78 = 7x + 8, so 7x = 70 and x = 10. Substitution confirms the result, so 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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