I'm working on a thought problem for an introductory discrete math course and seem to be stuck on how to solve this problem. If we have a poset:
$\bigl\langle\{2, 4, 6, 9, 12, 18, 27, 36, 48, 60, 72\},\: |\:\bigr\rangle,$
and impose a total order on the set such that the elements from least to greatest are: $2, 4, 18, 6, 27, 12, 36, 9, 72, 60, 48$,
is the total order compatible with the partial ordering of the divides relation? I know that if the elements in the poset are arranged in increasing order that it works, but I am not sure with this particular ordering. Can anyone help?