Changes

If we lay out this analysis of conjunction on the spreadsheet model of relational composition, the gist of it is the diagonal extension of a 2-adic ''loving'' relation <math>L \subseteq X \times Y</math> to the corresponding 3-adic ''being and loving'' relation <math>L \subseteq X \times X \times Y,</math> which is then composed in a specific way with a 2-adic ''serving'' relation <math>S \subseteq X \times Y,</math> so as to determine the 2-adic relation <math>L,\!S \subseteq X \times Y.</math>  Table&nbsp;15 schematizes the associated constraints on tuples.

If we lay out this analysis of conjunction on the spreadsheet model of relational composition, the gist of it is the diagonal extension of a 2-adic ''loving'' relation <math>L \subseteq X \times Y</math> to the corresponding 3-adic ''being and loving'' relation <math>L \subseteq X \times X \times Y,</math> which is then composed in a specific way with a 2-adic ''serving'' relation <math>S \subseteq X \times Y,</math> so as to determine the 2-adic relation <math>L,\!S \subseteq X \times Y.</math>  Table&nbsp;15 schematizes the associated constraints on tuples.

{| align="center" cellspacing="6" width="90%"

| align="center" |

 

{| align="center" cellpadding="10" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center; width:60%"

Table 15.  Conjunction Via Composition

|+ '''Table 15.  Conjunction Via Composition'''

o---------o---------o---------o---------o

|-

|         #  !1!   |   !1!   |   !1!   |

| style="border-right:1px solid black; border-bottom:1px solid black; width:25%" | &nbsp;

o=========o=========o=========o=========o

| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>

|   L,   #    X   |   X   |   Y   |

| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>

o---------o---------o---------o---------o

| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>

|   S    #        |   X   |   Y   |

|-

o---------o---------o---------o---------o

| style="border-right:1px solid black" | <math>L,\!</math>

| L , S #    X   |         |   Y   |

| <math>X\!</math>

| <math>X\!</math>

</pre>

| <math>Y\!</math>

|-

| style="border-right:1px solid black" | <math>S\!</math>

| &nbsp;

| <math>X\!</math>

| <math>Y\!</math>

|-

| style="border-right:1px solid black" | <math>L,\!S</math>

| <math>X\!</math>

| &nbsp;

| <math>Y\!</math>

|}

|}

===Commentary Note 10.11===

===Commentary Note 10.11===