 Solution

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

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

Because

P (x) \subseteq P (x)

, the relation is reflexive. If

x ⪯ y

and

y ⪯ z

, then

P (x) \subseteq P (y) \subseteq P (z),

so it is transitive. It is not symmetric: for

x = (1, 0, \dots, 0), y = (1, 1, 0, \dots, 0),

one has

x ⪯ y

but not

y ⪯ x

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