Sample Venn Diagram

Sample Venn diagram.
Venn diagrams are frequently used to build intuition for proofs. The diagrams are designed to present fairly general pictures of what is known, and these pictures can often help a person to see set-theoretic relationships. A good Venn diagram can be very useful, but a Venn diagram itself is not a proof. In particular, if a mistake is made in drawing the Venn diagram, it is often possible to think that a property is true when it really is not. In especially complicated cases, it may be very difficult to see whether the picture is correct. The picture may be vague on certain points as well. For example, Figure 1.2 suggests that there are elements of B that are in neither A nor C. This may or may not be true. Nevertheless, a good Venn diagram is valuable both in suggesting whether a statement could be true and in motivating and illustrating the proof.