E proposition

But for the corresponding I proposition to be true, there must be something in the central region. Thus, they cannot both be true. They also cannot both be false. The only way for an E proposition to be false is for there to be something in the central region, but then the corresponding I proposition is not false but true. The only way for the I proposition to be false is if there is nothing in the central region, and then the E proposition is not false but true. Thus, they cannot both be true, and they cannot both be false. In other words, they always have opposite truth values. This relation is described by saying that these propositions are contradictories.

More generally, we can produce a diagram for the denial of a proposition by a simple procedure. The only information given in a Venn diagram is represented either by shading out some region, thereby indicating that nothing exists in it, or by putting an asterisk in a region, thereby indicating that something does exist in it. We are given no information about regions that are unmarked. To represent the denial of a proposition, we simply re- verse the information in the diagram. That is, where there is an asterisk, we put in shading; where there is shading, we put in an asterisk. Everything else is left unchanged. Thus, we can see at once that corresponding E and I propositions are denials of one another, so they must always have opposite truth values. This makes them contradictories.