If n(A − B) = 3x + 2, n(B − A) = 2x + 5, n(A ∩ B) = x + 4, and n(A ∪ B) = 71, what is x?
Answer and explanation
Correct answer: 10
The three regions forming A ∪ B are A − B, B − A, and A ∩ B. These regions are pairwise disjoint, so their cardinalities can be added: 71 = (3x + 2) + (2x + 5) + (x + 4) = 6x + 11. Hence 6x = 60 and x = 10. With x = 10, the three region sizes are 32, 25, and 14, whose sum is 71; therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
The three regions forming A ∪ B are A − B, B − A, and A ∩ B. These regions are pairwise disjoint, so their cardinalities can be added: 71 = (3x + 2) + (2x + 5) + (x + 4) = 6x + 11. Hence 6x = 60 and x = 10. With x = 10, the three region sizes are 32, 25, and 14, whose sum is 71; therefore 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).
