Secondly, what of No. 6? Here we are a little better off. We know that there is something in it, for there is a

red counter in its outer portion. It is true we do not know whether its inner portion is empty or occupied: but what does that matter? One solitary Cake, in one corner of the Square, is quite sufficient excuse for saying "this Square is occupied", and for marking it with a red counter.

As to No. 7, we are in the same condition as with No. 5——we find it partly 'empty', but we do not know whether the other part is empty or occupied: so we dare not mark this Square.

And as to No. 8, we have simply no information at all.

The result is

Our 'Conclusion', then, must be got out of the rather meagre piece of information that there is a red counter in the ${\displaystyle xy^{\prime }}$-Square. Hence our Conclusion is "some ${\displaystyle x}$ are ${\displaystyle y^{\prime }}$", i.e. "some new Cakes are not-nice (Cakes)": or, if you prefer to take ${\displaystyle y^{\prime }}$ as your Subject, "some not-nice Cakes are new (Cakes)"; but the other looks neatest.

We will now write out the whole Syllogism, putting the symbol ∴ for "therefore", and omitting "Cakes", for the sake of brevity, at the end of each Proposition.