Simultaneously, the man may or may not be middle aged. But, by convention, we will not consider the possibility of a single person being either young, or middle aged, or neither. Here we are talking of simple propositions such that would correspond to a single circle on Venn diagrams. As an example, cakes may be fresh or not. No cakes are fresh.
All cakes are fresh.
And this is an example of what Lewis Carroll calls a particular proposition. For it talks only about a part of a set. In the latter examples, a natural universe of discourse is the set of all cakes . Bilateral diagram is Lewis Carroll's device to represent the situation in which objects are considered that may or may not have two properties. So that a cake may be fresh, or good, or neither, or both.