5. A set $M$ is called an ordered set if a binary relation, called order, denoted by $\leqslant$, is defined on it, satisfying the following conditions:
(1) Reflexivity: For all $x \in M$, $x \leqslant x$;
(2) Antisymmetry: If $x \leqslant y$ and $y \leqslant x$, then $x=y$;
(3) Transitivity: If $x \preccurlyeq y$ and $y \leqslant z$, then $x \preccurlyeq z$.
Furthermore, in an ordered set, $x \prec y$ means $x \leqslant y$ and $x \neq y$; $x \geqslant y$ means $y \leqslant x$; $x \succ y$ means $x \geqslant y$ and $x \neq y$. Prove:
(i) In an ordered set, at most one of $x=y$, $x \prec y$, $y \prec x$ holds.
(ii) If $x<y$, $y \prec z$, then $x \prec z$.
(iii) Let $S$ be a non-empty set, and $T$ be the set of all subsets of $S$. If the subset relation $A \subseteq B$ is used as the order $A \preccurlyeq B$, then $T$ is an ordered set.
(iv) In the usual set of non-negative integers, if the divisibility relation $a \mid b$ is used as the order $a \leqslant b$, then it is an ordered set (Note: For any two elements $x$, $y$ in the ordered set $M$, it is not necessary that $x \preccurlyeq y$ or $y \leqslant x$ holds; they can lack this order relation).