Some schools are colleges. Some colleges are educational institutions. Clearly we have to represent the second premise in a similar way, except that we need to x-x the areas where schools and colleges overlap. Some schools are educational institutions. Some schools are colleges.
Some colleges are educational institutions.
To use Venn diagrams to determine validity on the classical view, we need to alter the above account. Classical logic evidently assumes that, in sentences which express universal categorical statements, both the subject and predicate terms refer to existing objects. If we want to use Venn diagrams to determine validity on the classical view we need to add these assumptions to the diagram. Thus, if the statement is an A statement, besides shading the area of S that is not P, we must also add an X to the area where S and P overlap. Doing this, we obtain. . . .