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.
Some schools are colleges.
Some colleges are educational institutions. Then we need to represent the second premise. This premise tells us that there is at least one school that is also a college. To express this in the diagram, we need to place an x in those areas where schools and colleges overlap. The only such area that has not been shaded, however, is the area where the three rectangles overlap.