Note 7 — Front matter

This conclusion may be illustrated and verified by considering an example such as the following.

Let denote all steamers, or steam-vessels, denote all steamers, or armed vessels, denote all vessels of the Mediterranean.

Equation(a) would then express that armed steamers consist of the armed vessels of the Mediterranean and the steam-vessels not of the Mediterranean. From this it follows—

(1) That there are no armed vessels except steamers in the Mediterranean.

(2) That all unarmed steamers are in the Mediterranean (since the steam-vessels not of the Mediterranean are armed). Hence we infer that the vessels of the Mediterranean consist of all unarmed steamers; any number of armed steamers; and any number of unarmed vessels without steam. This, expressed symbolically, is equation (15).