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
$$
\boxed{\begin{aligned}
&\forall x\in X\;xRx,\\
&\forall x,y\in X\;(xRy\Rightarrow yRx),\\
&\forall x,y,z\in X\;((xRy\land yRz)\Rightarrow xRz).
\end{aligned}}
$$

Solution

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

 Solution (source code)