The way I understand minimal and maximal is the following.
Consider the following collection of sets:
{{1,2},{2,4},{1,6,7},{1,2,4,5,6},{8}}
The minimal members of this collection of sets is: {1,2},{2,4},{1,6,7},{8}
Meaning there are no other sets in the collection that are proper subsets of the set.
Minimal Set Example 1: in the set {1,2} this case holds true because the only proper subsets possible are {1} and {2}. Those sets {{1},{2}) are nowhere to be found in the collection. Therefore we include {1,2} as a part of the minimal collection of sets.
Minimal Set Example 2: in the set {1,6,7} this case holds true because the only proper subsets possible are {1},{6},{7},{1,6},{1,7}, and {6,7}. Those proper subsets ({1},{6},{7},{1,6},{1,7}, and {6,7}) are nowhere to be found in the collection. Therefore we include {1,6,7} as a part of the minimal collection of sets.
The maximal members of this collection of sets is: {1,6,7},{1,2,4,5,6},{8}
Meaning none of these sets are proper subsets of other sets in the collection. NOTICE: The maximal collection is not mutually exclusive of the minimum collection. See {1,6,7}.
Maximal Set Example 1: in the set {8} this case holds true because this set is not found to be a subset of any of the other sets in the collection. Meaning 8 is not found in any of the other sets in the collection. Therefore we include {8} as a part of the maximal collection of sets.
Maximal Set Example 2: in the set {1,6,7} this case holds true because this set is not found to be a subset of any of the other sets in the collection. Meaning all of the numbers of the set {1,6,7} are not found together as a part of another set in the collection. Therefore we include {1,6,7} as a part of the maximal collection of sets.
Best Answer
You missed the edges 24-72 and 4-36.
$\inf_A\{16,18\}$, if it exists, is the greatest lower bound of both 16 and 18. The lower bounds of 16 are $\{2,4,8\}$ and the lower bounds of 18 are $\{2,6\}$. 2 is the only common lower bound so it is the greatest and $\inf_A\{16,18\} = 2$.
A similar effort should show you that $\sup_A\{4,6\} = 24$.