= Solution
Inequality on a domain containing at least two people is \b[not] a <Euclidean relation>. Choose distinct people $a,b$ and put $x=a$, $y=z=b$. Both premises $a\ne b$ hold, but the conclusion would be $b\ne b$. Thus
$$
\boxed{\ne\text{ is not Euclidean on the domain of people}.}
$$
The possibility $y=z$ matters: the defining <universal quantifiers> do not require distinct arguments. On a domain with at most one element the inequality <binary relation> is empty and the condition holds by <vacuous truth>.
Back to article page
