# Page:Carroll - Game of Logic.djvu/36

Now suppose we divide our Universe of Things in three ways, with regard to three different Attributes. Out of these three Attributes, we may make up three different couples (for instance, if they were ${\displaystyle a}$, ${\displaystyle b}$, ${\displaystyle c}$, we might make up the three couples ${\displaystyle ab}$, ${\displaystyle ac}$, ${\displaystyle bc}$). Also suppose we have two Propositions given us, containing two of these three couples, and that from them we can prove a third Proposition containing the third couple. (For example, if we divide our Universe for ${\displaystyle m}$, ${\displaystyle x}$, and ${\displaystyle y}$ ; and if we have the two Propositions given us, "no ${\displaystyle m}$ are ${\displaystyle x^{\prime }}$" and "all ${\displaystyle m^{\prime }}$ are ${\displaystyle y}$", containing the two couples ${\displaystyle mx}$ and ${\displaystyle my}$, it might be possible to prove from them a third Proposition, containing ${\displaystyle x}$ and ${\displaystyle y}$.)