Changes

In other words, the proposition <math>q\!</math> is a truth-function of the 3 logical variables <math>u\!</math>, <math>v\!</math>, <math>w\!</math>, and it may be evaluated according to the "truth table" scheme that is shown in Table 2.  In this representation the polymorphous set <math>Q\!</math> appears in the guise of what some people call the "pre-image" or the "fiber of truth" under the function <math>q\!</math>.  More precisely, the 3-tuples for which <math>q\!</math> evaluates to true are in an obvious correspondence with the shaded cells of the venn diagram.  No matter how we get down to the level of actual information, it's all pretty much the same stuff.

In other words, the proposition <math>q\!</math> is a truth-function of the 3 logical variables <math>u\!</math>, <math>v\!</math>, <math>w\!</math>, and it may be evaluated according to the "truth table" scheme that is shown in Table 2.  In this representation the polymorphous set <math>Q\!</math> appears in the guise of what some people call the "pre-image" or the "fiber of truth" under the function <math>q\!</math>.  More precisely, the 3-tuples for which <math>q\!</math> evaluates to true are in an obvious correspondence with the shaded cells of the venn diagram.  No matter how we get down to the level of actual information, it's all pretty much the same stuff.

{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:60%"

 

{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:#f8f8ff; font-weight:bold; text-align:center; width:60%"

|+ '''Table 2.  Polymorphous Function ''q'' '''

|+ '''Table 2.  Polymorphous Function ''q'' '''

|- style="background:paleturquoise"

|- style="background:#e6e6ff"

! style="width:20%" | ''u v w''

! style="width:20%" | ''u v w''

! style="width:20%" | ''u'' &and; ''v''

! style="width:20%" | ''u'' &and; ''v''

| 1 1 1 || 1 || 1 || 1 || 1

| 1 1 1 || 1 || 1 || 1 || 1

|}

|}

With the pictures of the venn diagram and the truth table before us, we have come to the verge of seeing how the word "model" is used in logic, namely, to distinguish whatever things satisfy a description.

With the pictures of the venn diagram and the truth table before us, we have come to the verge of seeing how the word "model" is used in logic, namely, to distinguish whatever things satisfy a description.

Another common scheme for description and evaluation of a proposition is the so-called ''truth table'' or the ''semantic tableau'', for example:

Another common scheme for description and evaluation of a proposition is the so-called ''truth table'' or the ''semantic tableau'', for example:

{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:60%"

 

{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:#f8f8ff; font-weight:bold; text-align:center; width:60%"

|+ '''Table 2.  Truth Table for the Proposition ''q'' '''

|+ '''Table 2.  Truth Table for the Proposition ''q'' '''

|- style="background:paleturquoise"

|- style="background:#e6e6ff"

! style="width:20%" | ''u v w''

! style="width:20%" | ''u v w''

! style="width:20%" | ''u'' &and; ''v''

! style="width:20%" | ''u'' &and; ''v''

| 1 1 1 || 1 || 1 || 1 || 1

| 1 1 1 || 1 || 1 || 1 || 1

|}

|}

Reading off the shaded cells of the venn diagram or the rows of the truth table that have a "1" in the q column, we see that the ''models'', or satisfying interpretations, of the proposition <math>q\!</math> are the four that can be expressed, in either the ''additive'' or the ''multiplicative'' manner, as follows:

Reading off the shaded cells of the venn diagram or the rows of the truth table that have a "1" in the q column, we see that the ''models'', or satisfying interpretations, of the proposition <math>q\!</math> are the four that can be expressed, in either the ''additive'' or the ''multiplicative'' manner, as follows: