Solid fill areas in diagrams should be a striped pattern like this:

Venn diagrams provide an effective method for representing classes and propositions. Because every standard-form categorical proposition contains two classes, we begin our diagrams by drawing two overlapping circles like this:

We label the circles S and P to represent the classes designated by the subject term and the predicate term.

S P

Each region of the diagram corresponds to a possible relationship between the members of the subject class and the members of the predicate class. The region on the left, symbolized as SP-bar, corresponds to all things that are members of the subject class but not the predicate class. The overlapping region, symbolized SP, corresponds to all things that are members of both classes. The region on the right, symbolized S-barP corresponds to all things that are members of the predicate class but not the subject class. And finally, the region outside both circles, symbolized S-barP-bar, corresponds to the complement of both classes, or everything that is a member of neither the subject nor the predicate class.

S P

_ _

SP SP SP

_ _

SP

To diagram categorical propositions, we need a way to indicate which regions in the overlapping circles are empty and which have members. In Venn diagrams, shading indicates that a region is empty and an x indicates that it has members.

Now let’s look at an example. Consider the proposition "All seniors are prospects for employment." This is an A proposition, with the form "All S is P." It claims that every member of the subject class (seniors) is also a member of the predicate class (prospects for employment). In other words, there are no members of S that are outside P, or SP-bar equals zero. To represent this we shade the region that represents SP-bar to indicate that it is empty.

S P

All seniors are prospects for employment

_

A: All S is P (SP = 0)

The E proposition "No seniors are prospects for employment" has the form "No S is P." It claims that the overlapping region between the two classes, SP, is empty, which we indicate by shading the SP region in our diagram.

S P

No seniors are prospects for employment

E: No S is P (SP =0)

The I proposition "Some seniors are prospects for employment" has the form "Some S is P". It claims that there is at least one member of S that is also a P. In other words, the SP region has one or more members and is not empty, which we indicate with an x in the overlap between the circles.

S P

x

Some seniors are prospects for employment

I: Some S is P (SP ? 0)

Finally, the O proposition "Some seniors are not prospects for employment" has the form "Some S is not P". It claims that there is at least one member of S that is outside P. In other words, the segment of circle S that does not overlap with circle P has one or more members and is not empty. We show this by placing an x in that area representing SP-bar.

S P

x

Some survivors are manipulators

_

O: Some S is not P (SP ? 0)