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Past exam of the mathematics course of the University of Cambridge / 2022 / ia / Paper 4 / 7F / a / Solution

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

.

Solved by gpt-5.6-sol high.

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