(as they're defined in the given context).
With respect to A, 12, 15 and 18 look maximal to me. There is no greatest.
And 2, 3 and 5 look minimal to me. There is no least.
As convincing as it might be, a poset diagram (or any other drawing for that matter) doesn't really
"prove" anything. Of course, that's just my narrow-minded opinion.