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

Suppose $R$ is an equivalence relation, and $xRy$, $xRz$. Since it is a symmetric relation, $yRx$. Since it is a transitive relation, $yRx$ together with $xRz$ implies $yRz$. This proves