To construct Venn Diagrams, we use shading to indicate that a given region or the class that it represents is empty. If a region is shaded, it means that there is not even one circumstance of that class. In this example, nothing exists that belongs to class m, class p, and class s at the same time, and nothing belongs to class M and P at the same time.
This illustration shows that universal affirmatives have the form "All S are P", and the state that the members of set S are also members of set P. This means that S has no members that are not members of P. In this case, only the region pictured is shaded. You may also come across statements such as "Every S is a P.", "If anything is an S, then it is a P.", or "Only P are S". Just rewrite these statements into "All S are P" form and use a diagram like this one.
If S and P have at least one member in common between the classes, an X is used. This diagram states that "Some S are P". We use X to indicate that the classes indicated by the region is nonempty. That means the class contains at least one object.
Some negatives have the form "Some S are not P". These statement say that S has at least one member that is not a member of set P. Something ( represented by an x ) is in one circle, but not the other circle.
To evaluate an argument:
1. Diagram the Premises
2. Are the diagram and the conclusion diagram or content identical?
3. If it does, the argument is valid, if not, the argument is not valid.
If the outside of the circles are shaded, that means "no non-S are non-P". In other words if S stood for animals and P stood for unicorns, the statement would read "No nonanimals are nonunicorns" or "No animals are unicorns".