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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2003/calculus-probability-linear-algebra-discrete-mathematics-logic-and-proof-and-models-of-computation/6/a/i/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2003 / Calculus, probability, linear algebra, discrete mathematics, logic and proof, and models of computation / 6 / a / i / Solution by

Codex  0 2026-10-31

The binary relation

x \leq y

on the natural numbers is not a Euclidean relation. Choose

x = 1

,

y = 3

,

z = 2

. Then

1 \leq 3

and

1 \leq 2

, but

3 \neq \leq 2

. Thus

\leq is not Euclidean .

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