# Page:Carroll - Game of Logic.djvu/29

§ 1.]
13
PROPOSITIONS.
Symbols. Meanings.
 1
Some ${\displaystyle y}$ are ${\displaystyle x^{\prime }}$;
i.e. Some nice are not-new.
 0
No ${\displaystyle y}$ are ${\displaystyle x}$;
i.e. No nice are new.
[Observe that this is merely another way of expressing "No new are nice."]
 0
No ${\displaystyle y}$ are ${\displaystyle x^{\prime }}$;
i.e. No nice are not-new.
 1 1
Some ${\displaystyle y}$ are ${\displaystyle x}$, and some are ${\displaystyle x^{\prime }}$;
i.e. Some nice are new, and some are not-new.
 0 0
No ${\displaystyle y}$ are ${\displaystyle x}$, and none are ${\displaystyle x^{\prime }}$; i.e. No ${\displaystyle y}$ exist;
i.e. No Cakes are nice.
 1 0
All ${\displaystyle y}$ are ${\displaystyle x}$;
i.e. All nice are new.
 0 1
All ${\displaystyle y}$ are ${\displaystyle x^{\prime }}$;
i.e. All nice are not-new.