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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/b/ii/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 / b / ii / Solution by

Codex  0 2026-10-31

Suppose

R

is an equivalence relation, and

x R y

,

x R z

. Since it is a symmetric relation,

y R x

. Since it is a transitive relation,

y R x

together with

x R z

implies

y R z

. This proves

R an equivalence relation ⟹ R Euclidean .

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