Symbolic Logic

by Lewis Carroll

5. mx′₁ † ym₀ ¶ x′y′₁ [Fig. II.
i.e. “Some x′ are y′.”

6. x′m₀ † my₀ ¶ nothing.
[Fallacy of Like Eliminands not asserted to exist.]

7. mx′₀ † y′m₁ ¶ xy′₁ [Fig. II.
i.e. “Some x are y′.”

8. m′₁x₀ † m′y₀ ¶ x′y′₁ [Fig. III.
i.e. “Some x′ are y′.”

9. x′m′₁ † my₀ ¶ nothing.
[Fallacy of Unlike Eliminands with an Entity-Premiss.]

10. x₁m′₀ † y′₁m₀ ¶ x₁y′₀ † y′₁x₀ [Fig. I (β).
i.e. “All x are y, and all y′ are x′.”

11. mx₀ † y′₁m₀ ¶ nothing.
[Fallacy of Like Eliminands not asserted to exist.]

12. xm₀ † y₁m′₀ ¶ y₁x₀ [Fig. I (α).
i.e. “All y are x′.”

13. m′₁x′₀ † ym₀ ¶ x′y₀ [Fig. I.
i.e. “No x′ are y.”

14. m₁x′₀ † m′₁y′₀ ¶ x′y′₀ [Fig. I.
i.e. “No x′ are y′.”