 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ia/paper-4/7f/c/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

x \sim y ⟺ P (x) = P (y) .

Equality of sets is reflexive, symmetric, and transitive, so

\sim

is an equivalence relation. Its classes are indexed by all subsets of

{1, \dots, n}

, and every subset occurs as the support of its zero-one indicator vector. The number of classes is therefore

2^{n} .

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