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Directory talk:Jon Awbrey/Papers/Differential Propositional Calculus (view source)

Revision as of 13:24, 29 May 2008

40 bytes removed ,  13:24, 29 May 2008
→‎Work Area 3: change color scheme
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===Variant 2===
 
===Variant 2===
   −
{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:96%"
+
{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:mintcream; font-weight:bold; text-align:center; width:96%"
 
|+ '''Table 1.  Propositional Forms on Two Variables'''
 
|+ '''Table 1.  Propositional Forms on Two Variables'''
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|- style="background:paleturquoise"
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|- style="background:aliceblue"
 
| <p>&nbsp;</p>
 
| <p>&nbsp;</p>
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| align="right" | <p><math>x :\!</math></p>
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| align="right" | <p><math>x\!</math> :</p>
 
| <p>1 1 0 0</p>
 
| <p>1 1 0 0</p>
 
| <p>&nbsp;</p>
 
| <p>&nbsp;</p>
 
| <p>&nbsp;</p>
 
| <p>&nbsp;</p>
 
| <p>&nbsp;</p>
 
| <p>&nbsp;</p>
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|- style="background:paleturquoise"
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|- style="background:aliceblue"
 
| <p>&nbsp;</p>
 
| <p>&nbsp;</p>
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| align="right" | <p><math>y :\!</math></p>
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| align="right" | <p><math>y\!</math> :</p>
 
| <p>1 0 1 0</p>
 
| <p>1 0 1 0</p>
 
| <p>&nbsp;</p>
 
| <p>&nbsp;</p>
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<p><math>f_{1}\!</math></p><br>
 
<p><math>f_{1}\!</math></p><br>
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<p><math>f_{0001}\!</math></p><br>
 
<p><math>f_{0001}\!</math></p><br>
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<p>0 0 0 1</p><br>
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<p><math>(x)(y)\!</math></p><br>
 
<p><math>(x)(y)\!</math></p><br>
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|}
 
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|
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{| align="center" style="background:lightcyan"
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{| align="center" style="background:mintcream"
 
|
 
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<p>Neither x nor y</p><br>
 
<p>Neither x nor y</p><br>
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|}
 
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{| align="center" style="background:lightcyan"
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{| align="center" style="background:mintcream"
 
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<p><math>\lnot x \land \lnot y</math></p><br>
 
<p><math>\lnot x \land \lnot y</math></p><br>
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|-
 
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<p><math>f_{3}\!</math></p><br>
 
<p><math>f_{3}\!</math></p><br>
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|}
 
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<p><math>f_{0011}\!</math></p><br>
 
<p><math>f_{0011}\!</math></p><br>
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|}
 
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<p>0 0 1 1</p><br>
 
<p>0 0 1 1</p><br>
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<p><math>(x)\!</math></p><br>
 
<p><math>(x)\!</math></p><br>
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|}
 
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<p>Not x</p><br>
 
<p>Not x</p><br>
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<p><math>\lnot x</math></p><br>
 
<p><math>\lnot x</math></p><br>
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|-
 
|
 
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<p><math>f_{6}\!</math></p><br>
 
<p><math>f_{6}\!</math></p><br>
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<p><math>f_{0110}\!</math></p><br>
 
<p><math>f_{0110}\!</math></p><br>
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<p>0 1 1 0</p><br>
 
<p>0 1 1 0</p><br>
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<p><math>(x, y)\!</math></p><br>
 
<p><math>(x, y)\!</math></p><br>
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|}
 
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|
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{| align="center" style="background:mintcream"
 
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<p>x not equal to y</p><br>
 
<p>x not equal to y</p><br>
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<p><math>x \ne y</math></p><br>
 
<p><math>x \ne y</math></p><br>
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<p><math>f_{5}\!</math></p><br>
 
<p><math>f_{5}\!</math></p><br>
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<p><math>f_{0101}\!</math></p><br>
 
<p><math>f_{0101}\!</math></p><br>
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|}
 
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<p>0 1 0 1</p><br>
 
<p>0 1 0 1</p><br>
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<p><math>(y)\!</math></p><br>
 
<p><math>(y)\!</math></p><br>
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|}
 
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{| align="center" style="background:lightcyan"
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{| align="center" style="background:mintcream"
 
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<p>Not y</p><br>
 
<p>Not y</p><br>
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|}
 
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<p><math>\lnot y</math></p><br>
 
<p><math>\lnot y</math></p><br>
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|-
 
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{| align="center" style="background:lightcyan"
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{| align="center" style="background:mintcream"
 
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<p><math>f_{7}\!</math></p><br>
 
<p><math>f_{7}\!</math></p><br>
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|}
 
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<p><math>f_{0111}\!</math></p><br>
 
<p><math>f_{0111}\!</math></p><br>
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|}
 
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{| align="center" style="background:lightcyan"
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<p>0 1 1 1</p><br>
 
<p>0 1 1 1</p><br>
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<p><math>(x\ y)\!</math></p><br>
 
<p><math>(x\ y)\!</math></p><br>
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|}
 
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{| align="center" style="background:lightcyan"
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{| align="center" style="background:mintcream"
 
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<p>Not both x and y</p><br>
 
<p>Not both x and y</p><br>
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|}
 
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{| align="center" style="background:lightcyan"
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{| align="center" style="background:mintcream"
 
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<p><math>\lnot x \lor \lnot y</math></p><br>
 
<p><math>\lnot x \lor \lnot y</math></p><br>
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===Variant 3===
 
===Variant 3===
   −
{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:96%"
+
{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:mintcream; font-weight:bold; text-align:center; width:96%"
 
|+ '''Table 1.  Propositional Forms on Two Variables'''
 
|+ '''Table 1.  Propositional Forms on Two Variables'''
−
|- style="background:paleturquoise"
+
|- style="background:aliceblue"
 
| <p>&nbsp;</p>
 
| <p>&nbsp;</p>
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| align="right" | <p><math>x :\!</math></p>
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| align="right" | <p><math>x\!</math> :</p>
 
| <p>1 1 0 0</p>
 
| <p>1 1 0 0</p>
 
| <p>&nbsp;</p>
 
| <p>&nbsp;</p>
 
| <p>&nbsp;</p>
 
| <p>&nbsp;</p>
 
| <p>&nbsp;</p>
 
| <p>&nbsp;</p>
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|- style="background:aliceblue"
 
| <p>&nbsp;</p>
 
| <p>&nbsp;</p>
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| align="right" | <p><math>y :\!</math></p>
+
| align="right" | <p><math>y\!</math> :</p>
 
| <p>1 0 1 0</p>
 
| <p>1 0 1 0</p>
 
| <p>&nbsp;</p>
 
| <p>&nbsp;</p>
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|-
 
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<p><math>f_{1}\!</math></p>
 
<p><math>f_{1}\!</math></p>
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<p><math>f_{0001}\!</math></p>
 
<p><math>f_{0001}\!</math></p>
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|}
 
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<p>0 0 0 1</p>
 
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|}
 
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<p><math>(x)(y)\!</math></p>
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<p>Neither x nor y</p>
 
<p>Neither x nor y</p>
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<p><math>\lnot x \land \lnot y</math></p>
 
<p><math>\lnot x \land \lnot y</math></p>
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<p><math>f_{3}\!</math></p>
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<p><math>f_{0011}\!</math></p>
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<p><math>\lnot x</math></p>
 
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<p><math>f_{6}\!</math></p>
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<p><math>f_{0110}\!</math></p>
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<p><math>(x, y)\!</math></p>
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<p>x not equal to y</p>
 
<p>x not equal to y</p>
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<p><math>x \ne y</math></p>
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<p><math>f_{5}\!</math></p>
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<p><math>f_{0101}\!</math></p>
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<p><math>(y)\!</math></p>
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|}
 
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<p>Not y</p>
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<p><math>\lnot y</math></p>
 
<p><math>\lnot y</math></p>
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<p><math>f_{7}\!</math></p>
 
<p><math>f_{7}\!</math></p>
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<p><math>f_{0111}\!</math></p>
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<p>0 1 1 1</p>
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<p>Not both x and y</p>
 
<p>Not both x and y</p>
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{| align="center" style="background:mintcream"
 
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<p><math>\lnot x \lor \lnot y</math></p>
 
<p><math>\lnot x \lor \lnot y</math></p>
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===Variant 4===
 
===Variant 4===
   −
{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:96%"
+
{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:mintcream; font-weight:bold; text-align:center; width:96%"
 
|+ '''Table 1.  Propositional Forms on Two Variables'''
 
|+ '''Table 1.  Propositional Forms on Two Variables'''
−
|- style="background:paleturquoise"
+
|- style="background:purwablue"
 
|
 
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{| align="right" style="background:paleturquoise; text-align:right"
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{| align="right" style="background:purwablue; text-align:right"
 
| u :
 
| u :
 
|-
 
|-
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| 1100
 
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| f
 
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| &theta;f
 
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|
−
{| align="center" cellpadding="2" style="background:lightcyan"
+
{| align="center" cellpadding="2" style="background:mintcream"
 
| f<sub>0</sub>
 
| f<sub>0</sub>
 
|-
 
|-
Line 3,263: Line 3,263:  
|}
 
|}
 
|
 
|
−
{| align="center" cellpadding="2" style="background:lightcyan"
+
{| align="center" cellpadding="2" style="background:mintcream"
 
| 0000
 
| 0000
 
|-
 
|-
Line 3,281: Line 3,281:  
|}
 
|}
 
|
 
|
−
{| align="center" cellpadding="2" style="background:lightcyan"
+
{| align="center" cellpadding="2" style="background:mintcream"
 
| ()
 
| ()
 
|-
 
|-
Line 3,299: Line 3,299:  
|}
 
|}
 
|
 
|
−
{| align="center" cellpadding="2" style="background:lightcyan"
+
{| align="center" cellpadding="2" style="background:mintcream"
 
| ((&nbsp;f&nbsp;,&nbsp;&nbsp;&nbsp;&nbsp;()&nbsp;&nbsp;&nbsp;&nbsp;))
 
| ((&nbsp;f&nbsp;,&nbsp;&nbsp;&nbsp;&nbsp;()&nbsp;&nbsp;&nbsp;&nbsp;))
 
|-
 
|-
Line 3,317: Line 3,317:  
|}
 
|}
 
|
 
|
−
{| align="left" cellpadding="2" style="background:lightcyan; text-align:left"
+
{| align="left" cellpadding="2" style="background:mintcream; text-align:left"
 
| &nbsp;f + 1
 
| &nbsp;f + 1
 
|-
 
|-
Line 3,336: Line 3,336:  
|-
 
|-
 
|
 
|
−
{| align="center" cellpadding="2" style="background:lightcyan"
+
{| align="center" cellpadding="2" style="background:mintcream"
 
| f<sub>8</sub>
 
| f<sub>8</sub>
 
|-
 
|-
Line 3,354: Line 3,354:  
|}
 
|}
 
|
 
|
−
{| align="center" cellpadding="2" style="background:lightcyan"
+
{| align="center" cellpadding="2" style="background:mintcream"
 
| 1000
 
| 1000
 
|-
 
|-
Line 3,372: Line 3,372:  
|}
 
|}
 
|
 
|
−
{| align="center" cellpadding="2" style="background:lightcyan"
+
{| align="center" cellpadding="2" style="background:mintcream"
 
| &nbsp;&nbsp;u&nbsp;&nbsp;v&nbsp;&nbsp;
 
| &nbsp;&nbsp;u&nbsp;&nbsp;v&nbsp;&nbsp;
 
|-
 
|-
Line 3,390: Line 3,390:  
|}
 
|}
 
|
 
|
−
{| align="center" cellpadding="2" style="background:lightcyan"
+
{| align="center" cellpadding="2" style="background:mintcream"
 
| ((&nbsp;f&nbsp;,&nbsp;&nbsp;&nbsp;u&nbsp;&nbsp;v&nbsp;&nbsp;&nbsp;))
 
| ((&nbsp;f&nbsp;,&nbsp;&nbsp;&nbsp;u&nbsp;&nbsp;v&nbsp;&nbsp;&nbsp;))
 
|-
 
|-
Line 3,408: Line 3,408:  
|}
 
|}
 
|
 
|
−
{| align="left" cellpadding="2" style="background:lightcyan; text-align:left"
+
{| align="left" cellpadding="2" style="background:mintcream; text-align:left"
 
| &nbsp;f + uv + 1
 
| &nbsp;f + uv + 1
 
|-
 
|-
Jon Awbrey
12,080

edits

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