Changes

==Note 4==

==Note 4==

Last time we computed what is variously called the ''difference map'', the ''difference proposition'', or the ''local proposition'' <math>\operatorname{D}f_x</math> of the proposition <math>f(p, q) = pq\!</math> at the point <math>x\!</math> where <math>p = 1\!</math> and <math>q = 1.\!</math>

Last time we computed what will variously be called

the "difference map", the "difference proposition",

or the "local proposition" Df_x for the proposition

f<p, q> = pq at the point x where p = 1 and q = 1.

In the universe X = !P! x !Q!, the four propositions

In the universe <math>X = P \times Q,</math> the four propositions <math>pq,~ p \texttt{(} q \texttt{)},~ \texttt{(} p \texttt{)} q,~ \texttt{(} p \texttt{)(} q \texttt{)}</math> that indicate the "cells", or the smallest regions of the venn diagram, are called ''singular propositions''.  These serve as an alternative notation for naming the points <math>(1, 1),~ (1, 0),~ (0, 1),~ (0, 0),\!</math> respectively.

pq, p(q), (p)q, (p)(q) that indicate the "cells",

or the smallest regions of the venn diagram, are

called "singular propositions".  These serve as

an alternative notation for naming the points

<1, 1>, <1, 0>, <0, 1>, <0, 0>, respectively.

Thus, we can write Df_x = Df|x = Df|<1, 1> = Df|pq,

Thus we can write <math>\operatorname{D}f_x = \operatorname{D}f|x = \operatorname{D}f|(1, 1) = \operatorname{D}f|pq,</math> so long as we know the frame of reference in force.

so long as we know the frame of reference in force.

Sticking with the example f<p, q> = pq, let us compute the

In the example <math>f(p, q) = pq,\!</math> the value of the difference proposition <math>\operatorname{D}f_x</math> at each of the four points in <math>x \in X\!</math> may be computed in graphical fashion as shown below:

value of the difference proposition Df at all of the points.

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