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Revision as of 06:42, 24 December 2011
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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 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>
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.
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.
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.
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.
