In this Hasse-diagram is sup({36,72})={72} or is it non-existent? I think it might be {72} because {72} seems to be the upper bound of {36,72}. Then again, {72} seems to be the only upper bound, so who says it is the lowest upper bound, when there is only one upper bound?
And what about the infimum of {2,6}? Is it {2} or non-existent for the same reason?
And also, would it make any difference if {108} would be missing, so that
{72} would be the greatest element?
I think not, but I just want to be sure.
If there is only one upperbound then there is no upperbound that can be classified as 'lower'. That makes it the lowest upperbound. Here $72$ is the supremum of $36$ and $72$ and $2$ is the infimum of $2$ and $6$. As you are thinking: missing $108$ makes no difference here.