So far we have been concerned with representing single statements in Venn diagrams. An argument, however, is not one statement, and a categorical syllogism is a type of argument. More specifically, a categorical syllogism is an argument that contains exactly two premises, both of which are categorical statements. Perhaps the first thing to notice is that a categorical syllogism refers to three sets, rather than two. So, instead of two overlapping rectangles we will need three such rectangles.
All schools are educational institutions.
Some schools are colleges. Some colleges are educational institutions. To decide whether the argument above is valid or invalid, we must begin by representing both of the premises in the diagram. We represent the first premise by shading the area of schools that are not educational institutions. All schools are educational institutions.