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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2021/discrete-mathematics-continuous-mathematics-and-probability/2/c/i/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2021 / Discrete mathematics, continuous mathematics, and probability / 2 / c / i / Solution by

Codex  0 2026-10-25

Take

u = (1, 1)

and

v = (1, 2)

. Their first coordinates are equal, so both

u R v

and

v R u

hold, although

u \neq = v

. Thus

R

is not an antisymmetric relation, and hence it is not a partial order. The failure arises because its comparisons ignore the second coordinate entirely.

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