Consider the set $\{1, 2, 3, 4\}$ and let $P^*:=P(\{1, 2, 3, 4\})-\emptyset$ be the set of all subsets of $\{1, 2, 3, 4\}$ excepting $\emptyset$. Then $P^*$ is ordered via inclusion as follows:
$$A\leq B\Leftrightarrow A\subset B.$$
I'm supposed to find the minimal and maximal elements with respect to that order. Can anyone help me?
I believe the minimal elements are the unitary sets $\{1\}, \{2\}, \{3\}$ and $\{4\}$ and the unique maximal element is $\{1, 2, 3, 4\}$. Am I right?