An <equivalence relation> on a <set> $X$ is a <binary relation> that is <reflexive>, <symmetric> and <transitive>: every $x\in X$ satisfies $x\sim x$; $x\sim y$ implies $y\sim x$; and $x\sim y$, $y\sim z$ imply $x\sim z$. Each of these quantifiers ranges over the entire specified <set>. The separate entries below test these three properties.

Solution

Past exam of the mathematics course of the University of Cambridge / 2003 / ia / Paper 4 / 2C / Solution

 Solution (source code)