Let	x denote all steamers, or steam-vessels,
	y denote all armed vessels,
	z 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).