Some bars are not educational institutions. To represent the presuppositions that classical logic makes about the second premise, we must also add in our diagram that there exist some schools that are not bars and some bars that are not schools. However, we have already represented the first of these assumptions in the diagram. So all we need to do, then, is to represent the assumption that some bars exist that are not schools. We do this by x'ing the area of bars that are educational institutions and the area of bars that are not educational institutions, and drawing a line between them.
All schools are educational institutions.
No schools are bars. Some bars are not educational institutions. Inspecting the diagram we have now completed, we see that the conclusion of the argument does not follow from its premises. It is, therefore, invalid. All of this may seem clear enough, and so long as the things we are reasoning about exist, the principles of classical logic are acceptable.