Changes

<math>\begin{matrix}

<math>\begin{matrix}

\operatorname{Pr}_{12}^{-1}(P) & = & P \times Z & = & \{ (x, y, z) \in X \times Y \times Z : (x, y) \in P \}.

\operatorname{Pr}_{12}^{-1}(P) & = & P \times Z & = & \{ (x, y, z) \in X \times Y \times Z : (x, y) \in P \}.

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\\[4pt]

\operatorname{Pr}_{23}^{-1}(Q) & = & X \times Q & = & \{ (x, y, z) \in X \times Y \times Z : (y, z) \in Q \}.

\operatorname{Pr}_{23}^{-1}(Q) & = & X \times Q & = & \{ (x, y, z) \in X \times Y \times Z : (y, z) \in Q \}.

\end{matrix}</math>

\end{matrix}</math>

Regarded as logical models, the elements of the contension <math>P\!\!\And\!\!Q</math> satisfy the proposition referred to as the ''conjunction of extensions'' <math>P'\!</math> and <math>Q'.\!</math>

Regarded as logical models, the elements of the contension <math>P\!\!\And\!\!Q</math> satisfy the proposition referred to as the ''conjunction of extensions'' <math>P'\!</math> and <math>Q'.\!</math>

Next, the ''composition'' of <math>P\!</math> and <math>Q\!</math> is a dyadic relation <math>R' \subseteq X \times Z\!</math> that is notated as <math>R' = P \circ Q\!</math> and defined as follows.

Next, the "composition" of P and Q is a dyadic relation R' c XxZ that is notated as R' = P.Q and defined as follows:

P.Q = Pr13(P&Q) = {<x, z> C XxZ : <x, y, z> C P&Q}.

| <math>P \circ Q ~=~ \operatorname{Pr}_{13} (P\!\!\And\!\!Q) ~=~ \{ (x, z) \in X \times Z : (x, y, z) \in P\!\!\And\!\!Q \}.</math>

In other words:

In other words: