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Revision as of 03:40, 12 July 2007

712 bytes removed ,  03:40, 12 July 2007
→‎Table 65. Induced Transformation on Propositions
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o------------o----------o-----------o----------o------------o
 
o------------o----------o-----------o----------o------------o
 
</pre>
 
</pre>
−
  −
|    X%    |  <---  F  =  <f , g>  <---  |    U%    |
  −
o------------o----------o-----------o----------o------------o
  −
      
<br><font face="courier new">
 
<br><font face="courier new">
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|
 
|
 
{| cellpadding="2" style="background:lightcyan"
 
{| cellpadding="2" style="background:lightcyan"
−
| 0000
+
| ()
 
|-
 
|-
−
| 0001
+
| &nbsp;(u)(v)&nbsp;
 
|-
 
|-
−
| 0010
+
| &nbsp;(u)&nbsp;v&nbsp;&nbsp;
 
|-
 
|-
−
| 0011
+
| &nbsp;(u)&nbsp;&nbsp;&nbsp;&nbsp;
 
|-
 
|-
−
| 0100
+
| &nbsp;&nbsp;u&nbsp;(v)&nbsp;
 
|-
 
|-
−
| 0101
+
| &nbsp;&nbsp;&nbsp;&nbsp;(v)&nbsp;
 
|-
 
|-
−
| 0110
+
| &nbsp;(u,&nbsp;v)&nbsp;
 
|-
 
|-
−
| 0111
+
| &nbsp;(u&nbsp;&nbsp;v)&nbsp;
 
|}
 
|}
 
|
 
|
 
{| cellpadding="2" style="background:lightcyan"
 
{| cellpadding="2" style="background:lightcyan"
−
| ()
+
| 0 0 0 0
 
|-
 
|-
−
| &nbsp;(u)(v)&nbsp;
+
| 0 0 0 1
 
|-
 
|-
−
| &nbsp;(u)&nbsp;v&nbsp;&nbsp;
+
| 0 0 1 0
 
|-
 
|-
−
| &nbsp;(u)&nbsp;&nbsp;&nbsp;&nbsp;
+
| 0 0 1 1
 
|-
 
|-
−
| &nbsp;&nbsp;u&nbsp;(v)&nbsp;
+
| 0 1 0 0
 
|-
 
|-
−
| &nbsp;&nbsp;&nbsp;&nbsp;(v)&nbsp;
+
| 0 1 0 1
 
|-
 
|-
−
| &nbsp;(u,&nbsp;v)&nbsp;
+
| 0 1 1 0
 
|-
 
|-
−
| &nbsp;(u&nbsp;&nbsp;v)&nbsp;
+
| 0 1 1 1
 
|}
 
|}
 
|
 
|
 
{| cellpadding="2" style="background:lightcyan"
 
{| cellpadding="2" style="background:lightcyan"
−
| ((&nbsp;f&nbsp;,&nbsp;&nbsp;&nbsp;&nbsp;()&nbsp;&nbsp;&nbsp;&nbsp;))
+
| ()
 
|-
 
|-
−
| ((&nbsp;f&nbsp;,&nbsp;&nbsp;(u)(v)&nbsp;&nbsp;))
+
| &nbsp;(u)(v)&nbsp;
 
|-
 
|-
−
| ((&nbsp;f&nbsp;,&nbsp;&nbsp;(u)&nbsp;v&nbsp;&nbsp;&nbsp;))
+
| &nbsp;(u)&nbsp;v&nbsp;&nbsp;
 
|-
 
|-
−
| ((&nbsp;f&nbsp;,&nbsp;&nbsp;(u)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;))
+
| &nbsp;(u)&nbsp;&nbsp;&nbsp;&nbsp;
 
|-
 
|-
−
| ((&nbsp;f&nbsp;,&nbsp;&nbsp;&nbsp;u&nbsp;(v)&nbsp;&nbsp;))
+
| &nbsp;&nbsp;u&nbsp;(v)&nbsp;
 
|-
 
|-
−
| ((&nbsp;f&nbsp;,&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(v)&nbsp;&nbsp;))
+
| &nbsp;&nbsp;&nbsp;&nbsp;(v)&nbsp;
 
|-
 
|-
−
| ((&nbsp;f&nbsp;,&nbsp;&nbsp;(u,&nbsp;v)&nbsp;&nbsp;))
+
| &nbsp;(u,&nbsp;v)&nbsp;
 
|-
 
|-
−
| ((&nbsp;f&nbsp;,&nbsp;&nbsp;(u&nbsp;&nbsp;v)&nbsp;&nbsp;))
+
| &nbsp;(u&nbsp;&nbsp;v)&nbsp;
 
|}
 
|}
 
|
 
|
−
{| align="left" cellpadding="2" style="background:lightcyan; text-align:left"
+
{| cellpadding="2" style="background:lightcyan"
−
| &nbsp;f + 1
+
| f<sub>0</sub>
 
|-
 
|-
−
| &nbsp;f + u + v + uv
+
| f<sub>1</sub>
 
|-
 
|-
−
| &nbsp;f + v + uv + 1
+
| f<sub>2</sub>
 
|-
 
|-
−
| &nbsp;f + u
+
| f<sub>3</sub>
 
|-
 
|-
−
| &nbsp;f + u + uv + 1
+
| f<sub>4</sub>
 
|-
 
|-
−
| &nbsp;f + v
+
| f<sub>5</sub>
 
|-
 
|-
−
| &nbsp;f + u + v + 1
+
| f<sub>6</sub>
 
|-
 
|-
−
| &nbsp;f + uv
+
| f<sub>7</sub>
 
|}
 
|}
 
|-
 
|-
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|
 
|
 
{| cellpadding="2" style="background:lightcyan"
 
{| cellpadding="2" style="background:lightcyan"
−
| 1000
+
| &nbsp;&nbsp;u&nbsp;&nbsp;v&nbsp;&nbsp;
 
|-
 
|-
−
| 1001
+
| ((u,&nbsp;v))
 
|-
 
|-
−
| 1010
+
| &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;v&nbsp;&nbsp;
 
|-
 
|-
−
| 1011
+
| &nbsp;(u&nbsp;(v))
 
|-
 
|-
−
| 1100
+
| &nbsp;&nbsp;u&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 
|-
 
|-
−
| 1101
+
| ((u)&nbsp;v)&nbsp;
 
|-
 
|-
−
| 1110
+
| ((u)(v))
 
|-
 
|-
−
| 1111
+
| (())
 
|}
 
|}
 
|
 
|
 
{| cellpadding="2" style="background:lightcyan"
 
{| cellpadding="2" style="background:lightcyan"
−
| &nbsp;&nbsp;u&nbsp;&nbsp;v&nbsp;&nbsp;
+
| 1 0 0 0
 
|-
 
|-
−
| ((u,&nbsp;v))
+
| 1 0 0 1
 
|-
 
|-
−
| &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;v&nbsp;&nbsp;
+
| 1 0 1 0
 
|-
 
|-
−
| &nbsp;(u&nbsp;(v))
+
| 1 0 1 1
 
|-
 
|-
−
| &nbsp;&nbsp;u&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+
| 1 1 0 0
 
|-
 
|-
−
| ((u)&nbsp;v)&nbsp;
+
| 1 1 0 1
 
|-
 
|-
−
| ((u)(v))
+
| 1 1 1 0
 
|-
 
|-
−
| (())
+
| 1 1 1 1
 
|}
 
|}
 
|
 
|
 
{| cellpadding="2" style="background:lightcyan"
 
{| cellpadding="2" style="background:lightcyan"
−
| ((&nbsp;f&nbsp;,&nbsp;&nbsp;&nbsp;u&nbsp;&nbsp;v&nbsp;&nbsp;&nbsp;))
+
| &nbsp;&nbsp;u&nbsp;&nbsp;v&nbsp;&nbsp;
 
|-
 
|-
−
| ((&nbsp;f&nbsp;,&nbsp;((u,&nbsp;v))&nbsp;))
+
| ((u,&nbsp;v))
 
|-
 
|-
−
| ((&nbsp;f&nbsp;,&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;v&nbsp;&nbsp;&nbsp;))
+
| &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;v&nbsp;&nbsp;
 
|-
 
|-
−
| ((&nbsp;f&nbsp;,&nbsp;&nbsp;(u&nbsp;(v))&nbsp;))
+
| &nbsp;(u&nbsp;(v))
 
|-
 
|-
−
| ((&nbsp;f&nbsp;,&nbsp;&nbsp;&nbsp;u&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;))
+
| &nbsp;&nbsp;u&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 
|-
 
|-
−
| ((&nbsp;f&nbsp;,&nbsp;((u)&nbsp;v)&nbsp;&nbsp;))
+
| ((u)&nbsp;v)&nbsp;
 
|-
 
|-
−
| ((&nbsp;f&nbsp;,&nbsp;((u)(v))&nbsp;))
+
| ((u)(v))
 
|-
 
|-
−
| ((&nbsp;f&nbsp;,&nbsp;&nbsp;&nbsp;(())&nbsp;&nbsp;&nbsp;))
+
| (())
 
|}
 
|}
 
|
 
|
−
{| align="left" cellpadding="2" style="background:lightcyan; text-align:left"
+
{| cellpadding="2" style="background:lightcyan"
−
| &nbsp;f + uv + 1
+
| f<sub>8</sub>
 
|-
 
|-
−
| &nbsp;f + u + v
+
| f<sub>9</sub>
 
|-
 
|-
−
| &nbsp;f + v + 1
+
| f<sub>10</sub>
 
|-
 
|-
−
| &nbsp;f + u + uv
+
| f<sub>11</sub>
 
|-
 
|-
−
| &nbsp;f + u + 1
+
| f<sub>12</sub>
 
|-
 
|-
−
| &nbsp;f + v + uv
+
| f<sub>13</sub>
 
|-
 
|-
−
| &nbsp;f + u + v + uv + 1
+
| f<sub>14</sub>
 
|-
 
|-
−
| &nbsp;f
+
| f<sub>15</sub>
 
|}
 
|}
 
|}
 
|}
Jon Awbrey
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