| | | | | |
| .---|---. | |---|---|
| |(O)|(O)| | |(I)| |
|---|---|---|---| .-------.
| |(I)| | |
| .---|---. | .'. x'y_{1}
| | |
.---------------.

In this case we see that the Conclusion is an Entity, and that the
Nullity-Retinend has changed its Sign.

And we should find this Rule to hold good with _any_ Pair of Premisses
which fulfil the given conditions.

[The Reader had better satisfy himself of this, by working out,
on Diagrams, several varieties, such as

x'm_{0} + ym_{1} (which > xy_{1})
x_{1}m'_{0} + y'm'_{1} (which > x'y'_{1})
m_{1}x_{0} + y'm_{1} (which > x'y'_{1}).]

The Formula, to be remembered, is,

xm_{0} + ym_{1} > x'y_{1}

with the following Rule:--

_A Nullity and an Entity, with Like Eliminands, yield an
Entity, in which the Nullity-Retinend changes its Sign._

[Note that this Rule is merely the Formula expressed in words.]

pg077
Fig. III.

This includes any Pair of Premisses which are both of them Nullities,
and which contain Like Eliminands asserted to exist.

The simplest case is

xm_{0} + ym_{0} + m_{1}

[Note that "m_{1}" is here stated _separately_, because it does
not matter in which of the two Premisses it occurs: so that this
includes the _three_ forms "m_{1}x_{0} + ym_{0}", "xm_{0} +
m_{1}y_{0}", and "m_{1}x_{0} + m_{1}y_{0}".]

.---------------. .-------.
| | | | | |
| .---|---. | |---|---|
| |(O)|(O)| | | |(I)|
|---|---|---|---| .-------.
| |(O)|(I)| |
| .---|---. | .'. x'y'_{1}
| | |
.---------------.

In this case we see that the Conclusion is an Entity, and that _both_
Retinends have changed their Signs.

And we should find this Rule to hold good with _any_ Pair of Premisses
which fulfil the given conditions.

[The Reader had better satisfy himself of this, by working out,
on Diagrams, several varieties, such as

x'm_{0} + m_{1}y_{0} (which > xy'_{1})
m'_{1}x_{0} + m'y'_{0} (which > x'y_{1})
m_{1}x'_{0} + m_{1}y'_{0} (which > xy_{1}).]

The Formula, to be remembered, is

xm_{0} + ym_{0} + m_{1} > x'y'_{1}

with the following Rule (which is merely the Formula expressed in
words):--

_Two Nullities, wi