 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2002/ia/paper-4/6f/b/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

Take the finite ambient set

S = ⋃_{i} A_{i}

and the additive set function

f (A) = ∣ A ∣

. Disjoint subsets have additive cardinality, so (a) applies and gives

i = 1 ⋃ n A_{i} = \emptyset \neq = J \subseteq {1, \dots, n} \sum (- 1)^{∣ J ∣ + 1} j \in J ⋂ A_{j} .

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