Symbolic Logic

by Lewis Carroll

If either Retinend is asserted in the Premisses to exist, of course it may be so asserted in the Conclusion.

Hence we get two Variants of Fig. I, viz.

(α) where one Retinend is so asserted;

(β) where both are so asserted.

[The Reader had better work out, on Diagrams, examples of these two Variants, such as

m₁x₀ † y₁m′₀ (which proves y₁x₀)
x₁m′₀ † m₁y₀ (which proves x₁y₀)
x′₁m₀ † y₁m′₀ (which proves x′₁y₀ † y₁x′₀).]

The Formula, to be remembered, is

xm₀ † ym′₀ ¶ xy₀

with the following two Rules:—

(1) Two Nullities, with Unlike Eliminands, yield a Nullity, in which both Retinends keep their Signs.

[pg076](2) A Retinend, asserted in the Premisses to exist, may be so asserted in the Conclusion.