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Revision as of 13:54, 12 July 2007

3,081 bytes added ,  13:54, 12 July 2007
→‎Table 65. Induced Transformation on Propositions: make extra copy
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</pre>
 
</pre>
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<br><font face="courier new">
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{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:96%"
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|+ Table 65.  Induced Transformation on Propositions
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|- style="background:paleturquoise"
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| ''X''<sup>&nbsp;&bull;</sup>
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| colspan="3" |
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{| align="center" border="0" cellpadding="4" cellspacing="0" style="background:paleturquoise; font-weight:bold; text-align:center; width:80%"
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| &larr;
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| ''F''&nbsp;=&nbsp;‹''f''&nbsp;,&nbsp;''g''›
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| &larr;
 +
|}
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| ''U''<sup>&nbsp;&bull;</sup>
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|- style="background:paleturquoise"
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| ''f''<sub>''i''</sub>‹''x'',&nbsp;''y''›
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|
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{|
 +
|
 +
{|
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| u =
 +
|-
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| v =
 +
|}
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|-
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|
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{|
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| x =
 +
|-
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| y =
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|}
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|}
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|
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{|
 +
|
 +
{|
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| 1 1 0 0
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|-
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| 1 0 1 0
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|}
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|-
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|
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{|
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| 1 1 1 0
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|-
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| 1 0 0 1
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|}
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|}
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|
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{|
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|
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{|
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| = u
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|-
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| = v
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|}
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|-
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|
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{|
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| = f‹u,&nbsp;v›
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|-
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| = g‹u,&nbsp;v›
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|}
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|}
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| ''f''<sub>''j''</sub>‹''u'',&nbsp;''v''›
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|-
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|
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{| cellpadding="2" style="background:lightcyan"
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| f<sub>0</sub>
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|-
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| f<sub>1</sub>
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|-
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| f<sub>2</sub>
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|-
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| f<sub>3</sub>
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|-
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| f<sub>4</sub>
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|-
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| f<sub>5</sub>
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|-
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| f<sub>6</sub>
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|-
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| f<sub>7</sub>
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|}
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|
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{| cellpadding="2" style="background:lightcyan"
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| ()
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|-
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| &nbsp;(x)(y)&nbsp;
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|-
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| &nbsp;(x)&nbsp;y&nbsp;&nbsp;
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|-
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| &nbsp;(x)&nbsp;&nbsp;&nbsp;&nbsp;
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|-
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| &nbsp;&nbsp;x&nbsp;(y)&nbsp;
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|-
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| &nbsp;&nbsp;&nbsp;&nbsp;(y)&nbsp;
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|-
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| &nbsp;(x,&nbsp;y)&nbsp;
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|-
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| &nbsp;(x&nbsp;&nbsp;y)&nbsp;
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|}
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|
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{| cellpadding="2" style="background:lightcyan"
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| 0 0 0 0
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|-
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| 0 0 0 1
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|-
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| 0 0 1 0
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|-
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| 0 0 1 1
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|-
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| 0 1 0 0
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|-
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| 0 1 0 1
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|-
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| 0 1 1 0
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|-
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| 0 1 1 1
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|}
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|
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{| cellpadding="2" style="background:lightcyan"
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| ()
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|-
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| ()
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|-
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| &nbsp;(u)(v)&nbsp;
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|-
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| &nbsp;(u)(v)&nbsp;
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|-
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| &nbsp;(u,&nbsp;v)&nbsp;
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|-
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| &nbsp;(u,&nbsp;v)&nbsp;
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|-
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| &nbsp;(u&nbsp;&nbsp;v)&nbsp;
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|-
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| &nbsp;(u&nbsp;&nbsp;v)&nbsp;
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|}
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|
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{| cellpadding="2" style="background:lightcyan"
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| f<sub>0</sub>
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|-
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| f<sub>0</sub>
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|-
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| f<sub>1</sub>
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|-
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| f<sub>1</sub>
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|-
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| f<sub>6</sub>
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|-
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| f<sub>6</sub>
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|-
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| f<sub>7</sub>
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|-
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| f<sub>7</sub>
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|}
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|-
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|
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{| cellpadding="2" style="background:lightcyan"
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| f<sub>8</sub>
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|-
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| f<sub>9</sub>
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|-
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| f<sub>10</sub>
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|-
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| f<sub>11</sub>
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|-
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| f<sub>12</sub>
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|-
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| f<sub>13</sub>
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|-
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| f<sub>14</sub>
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|-
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| f<sub>15</sub>
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|}
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|
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{| cellpadding="2" style="background:lightcyan"
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| &nbsp;&nbsp;x&nbsp;&nbsp;y&nbsp;&nbsp;
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|-
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| ((x,&nbsp;y))
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|-
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| &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;y&nbsp;&nbsp;
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|-
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| &nbsp;(x&nbsp;(y))
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|-
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| &nbsp;&nbsp;x&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
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|-
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| ((x)&nbsp;y)&nbsp;
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|-
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| ((x)(y))
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|-
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| (())
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|}
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|
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{| cellpadding="2" style="background:lightcyan"
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| 1 0 0 0
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|-
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| 1 0 0 1
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|-
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| 1 0 1 0
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|-
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| 1 0 1 1
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|-
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| 1 1 0 0
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|-
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| 1 1 0 1
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|-
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| 1 1 1 0
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|-
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| 1 1 1 1
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|}
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|
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{| cellpadding="2" style="background:lightcyan"
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| &nbsp;&nbsp;u&nbsp;&nbsp;v&nbsp;&nbsp;
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|-
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| &nbsp;&nbsp;u&nbsp;&nbsp;v&nbsp;&nbsp;
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|-
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| ((u,&nbsp;v))
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|-
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| ((u,&nbsp;v))
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|-
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| ((u)(v))
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|-
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| ((u)(v))
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|-
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| (())
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|-
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| (())
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|}
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|
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{| cellpadding="2" style="background:lightcyan"
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| f<sub>8</sub>
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|-
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| f<sub>8</sub>
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|-
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| f<sub>9</sub>
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|-
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| f<sub>9</sub>
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|-
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| f<sub>14</sub>
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|-
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| f<sub>14</sub>
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|-
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| f<sub>15</sub>
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|-
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| f<sub>15</sub>
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|}
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|}
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</font><br>
    
<br><font face="courier new">
 
<br><font face="courier new">
Jon Awbrey
12,080

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