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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/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 / b / i / Solution by

Codex  0 2026-10-31

A binary relation

R

on a set

X

is an equivalence relation when it is a reflexive relation, a symmetric relation, and a transitive relation. In first-order logic, these three requirements are

\forall x \in X x R x, \forall x, y \in X (x R y \Rightarrow y R x), \forall x, y, z \in X ((x R y \land y R z) \Rightarrow x R z) .

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