| Line 9,220: |
Line 9,220: |
| | | ''U''<sup> •</sup> | | | ''U''<sup> •</sup> |
| | |- style="background:paleturquoise" | | |- style="background:paleturquoise" |
| − | | ''f''<sub>''i''</sub>‹''x'', ''y''› | + | | rowspan="2" | ''f''<sub>''i''</sub>‹''x'', ''y''› |
| − | |
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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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| − | | x =
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| − | |-
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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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| − | |
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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, v›
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| − | |-
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| − | | = g‹u, v›
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| − | |}
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| − | |}
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| − | | ''f''<sub>''j''</sub>‹''u'', ''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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| − | | (x)(y)
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| − | |-
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| − | | (x) y
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| − | |-
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| − | | (x)
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| − | |-
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| − | | x (y)
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| − | |-
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| − | | (y)
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| − | |-
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| − | | (x, y)
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| − | |-
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| − | | (x y)
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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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| − | | (u)(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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| − | | (u, 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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| − | {| 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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| − | | x y
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| − | |-
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| − | | ((x, y))
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| − | |-
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| − | | y
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| − | |-
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| − | | (x (y))
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| − | |-
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| − | | x
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| − | |-
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| − | | ((x) y)
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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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| − | | u 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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| − | | ((u, 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>
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| − | | |
| − | {| border=1
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| | | | | | |
| | {| | | {| |
| Line 9,474: |
Line 9,239: |
| | | = v | | | = v |
| | |} | | |} |
| | + | | rowspan="2" | ''f''<sub>''j''</sub>‹''u'', ''v''› |
| | |- | | |- |
| | | | | | |
| Line 9,493: |
Line 9,259: |
| | | = g‹u, v› | | | = g‹u, v› |
| | |} | | |} |
| − | |}
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| − | <br>
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| − |
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| − |
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| − | <br><font face="courier new">
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| − | {| align="center" border="1" cellpadding="0" 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> •</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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| − | | ←
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| − | | ''F'' = ‹''f'' , ''g''›
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| − | | ←
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| − | |}
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| − | | ''U''<sup> •</sup>
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| − | |- style="background:paleturquoise"
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| − | | ''f''<sub>''i''</sub>‹''x'', ''y''›
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| − | | colspan="3" |
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| − | {| align="center" border="1" cellpadding="0" cellspacing="0" style="background:paleturquoise; font-weight:bold; text-align:center; width:100%"
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| − | | width=33% |
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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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| − | | width=33% |
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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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| − | | width=33% |
| |
| − | {|
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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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| − | | width=33% |
| |
| − | {|
| |
| − | | x =
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| − | |-
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| − | | y =
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| − | |}
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| − | | width=33% |
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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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| − | | width=33% |
| |
| − | {|
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| − | | = f‹u, v›
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| − | |-
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| − | | = g‹u, v›
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| − | |}
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| − | |}
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| − | | ''f''<sub>''j''</sub>‹''u'', ''v''›
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| | |- | | |- |
| | | | | | |