Symbolic Logic

by Lewis Carroll

25. mx′₁ † my′₀ ¶ x′y₁ [Fig. II.
i.e. “Some x′ are y.”

26. mx′₀ † y₁m′₀ ¶ y₁x′₀ [Fig. I (α).
i.e. “All y are x.”

27. x₁m₀ † y′₁m′₀ ¶ (x₁y′₀ † y′₁x₀) [Fig. I (β).
i.e. “All x are y, and all y′ are x′.”

28. m₁x₀ † my₁ ¶ x′y₁ [Fig. II.
i.e. “Some x′ are y.”

29. mx₀ † y₁m₀ ¶ nothing.
[Fallacy of Like Eliminands not asserted to exist.]

30. x₁m₀ † ym₁ ¶ x′y₁ [Fig. II.
i.e. “Some y are x′.”

31. x₁m′₀ † y₁m′₀ ¶ nothing.
[Fallacy of Like Eliminands not asserted to exist.]

[pg147]32. xm′₀ † m₁y′₀ ¶ xy′₀ [Fig. I.
i.e. “No x are y′.”

33. mx₀ † my₀ ¶ nothing.
[Fallacy of Like Eliminands not asserted to exist.]

34. mx′₀ † ym₁ ¶ xy₁ [Fig. II.
i.e. “Some x are y.”