Let $\Pi(M)$ be the set of partitions of the set $M$. On $\Pi(M)$ we define the relation $\leq$ like so. For $\pi, \pi' \in \Pi(M)$ we say $\pi \leq \pi'$ applies when for all $A \in \pi$ and $B\in\pi'$ with $A \subseteq B$.
(i) Show:$\leq$ is a partially set of orders on $\Pi(M)$. (already solved this one)
(ii) Determine the Set $M$, so that $\leq$ is a total set of orders. (I think i solved this one but im not quite sure) I got that $A,B\in\pi$.
(iii) Show: Is $M=\{1,...,n\}$, are $\pi_1,...,\pi_r \in\Pi(M)$ different in pairs and when $\pi_1\leq\pi_2\leq···\leq\pi_r$ applies, then $r \leq n$.
i really dont know how i should do (iii)