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====New Versions====
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{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:90%"
|+ '''Table 1. Propositional Forms on Two Variables'''
|- style="background:paleturquoise"
! style="width:15%" | L<sub>1</sub>
! style="width:15%" | L<sub>2</sub>
! style="width:15%" | L<sub>3</sub>
! style="width:15%" | L<sub>4</sub>
! style="width:25%" | L<sub>5</sub>
! style="width:15%" | L<sub>6</sub>
|- style="background:paleturquoise"
|
| align="right" | x :
| 1 1 0 0
|
|
|
|- style="background:paleturquoise"
|
| align="right" | y :
| 1 0 1 0
|
|
|
|-
| f<sub>0</sub> || f<sub>0000</sub> || 0 0 0 0 || ( ) || false || 0
|-
| f<sub>1</sub> || f<sub>0001</sub> || 0 0 0 1 || (x)(y) || neither x nor y || ¬x ∧ ¬y
|-
| f<sub>2</sub> || f<sub>0010</sub> || 0 0 1 0 || (x) y || y and not x || ¬x ∧ y
|-
| f<sub>3</sub> || f<sub>0011</sub> || 0 0 1 1 || (x) || not x || ¬x
|-
| f<sub>4</sub> || f<sub>0100</sub> || 0 1 0 0 || x (y) || x and not y || x ∧ ¬y
|-
| f<sub>5</sub> || f<sub>0101</sub> || 0 1 0 1 || (y) || not y || ¬y
|-
| f<sub>6</sub> || f<sub>0110</sub> || 0 1 1 0 || (x, y) || x not equal to y || x ≠ y
|-
| f<sub>7</sub> || f<sub>0111</sub> || 0 1 1 1 || (x y) || not both x and y || ¬x ∨ ¬y
|-
| f<sub>8</sub> || f<sub>1000</sub> || 1 0 0 0 || x y || x and y || x ∧ y
|-
| f<sub>9</sub> || f<sub>1001</sub> || 1 0 0 1 || ((x, y)) || x equal to y || x = y
|-
| f<sub>10</sub> || f<sub>1010</sub> || 1 0 1 0 || y || y || y
|-
| f<sub>11</sub> || f<sub>1011</sub> || 1 0 1 1 || (x (y)) || not x without y || x → y
|-
| f<sub>12</sub> || f<sub>1100</sub> || 1 1 0 0 || x || x || x
|-
| f<sub>13</sub> || f<sub>1101</sub> || 1 1 0 1 || ((x) y) || not y without x || x ← y
|-
| f<sub>14</sub> || f<sub>1110</sub> || 1 1 1 0 || ((x)(y)) || x or y || x ∨ y
|-
| f<sub>15</sub> || f<sub>1111</sub> || 1 1 1 1 || (( )) || true || 1
|}
<br>
{| align="center" border="1" cellpadding="6" cellspacing="0" style="font-weight:bold; text-align:center; width:90%"
|+ '''Table 14. Differential Propositions'''
|- style="background:ghostwhite"
|
| align="right" | A :
| 1 1 0 0
|
|
|
|- style="background:ghostwhite"
|
| align="right" | dA :
| 1 0 1 0
|
|
|
|-
| f<sub>0</sub>
| g<sub>0</sub>
| 0 0 0 0
| ( )
| False
| 0
|-
|
{|
|
<br>
<br>
<br>
|}
|
{|
|
g<sub>1</sub><br>
g<sub>2</sub><br>
g<sub>4</sub><br>
g<sub>8</sub>
|}
|
{|
|
0 0 0 1<br>
0 0 1 0<br>
0 1 0 0<br>
1 0 0 0
|}
|
{|
|
(A)(dA)<br>
(A) dA <br>
A (dA)<br>
A dA
|}
|
{|
|
Neither A nor dA<br>
Not A but dA<br>
A but not dA<br>
A and dA
|}
|
{|
|
¬A ∧ ¬dA<br>
¬A ∧ dA<br>
A ∧ ¬dA<br>
A ∧ dA
|}
|-
|
{|
|
f<sub>1</sub><br>
f<sub>2</sub>
|}
|
{|
|
g<sub>3</sub><br>
g<sub>12</sub>
|}
|
{|
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0 0 1 1<br>
1 1 0 0
|}
|
{|
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(A)<br>
A
|}
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{|
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Not A<br>
A
|}
|
{|
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¬A<br>
A
|}
|-
|
{|
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<br>
|}
|
{|
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g<sub>6</sub><br>
g<sub>9</sub>
|}
|
{|
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0 1 1 0<br>
1 0 0 1
|}
|
{|
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(A, dA)<br>
((A, dA))
|}
|
{|
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A not equal to dA<br>
A equal to dA
|}
|
{|
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A ≠ dA<br>
A = dA
|}
|-
|
{|
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<br>
|}
|
{|
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g<sub>5</sub><br>
g<sub>10</sub>
|}
|
{|
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0 1 0 1<br>
1 0 1 0
|}
|
{|
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(dA)<br>
dA
|}
|
{|
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Not dA<br>
dA
|}
|
{|
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¬dA<br>
dA
|}
|-
|
{|
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<br>
<br>
<br>
|}
|
{|
|
g<sub>7</sub><br>
g<sub>11</sub><br>
g<sub>13</sub><br>
g<sub>14</sub>
|}
|
{|
|
0 1 1 1<br>
1 0 1 1<br>
1 1 0 1<br>
1 1 1 0
|}
|
{|
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(A dA)<br>
(A (dA))<br>
((A) dA)<br>
((A)(dA))
|}
|
{|
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Not both A and dA<br>
Not A without dA<br>
Not dA without A<br>
A or dA
|}
|
{|
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¬A ∨ ¬dA<br>
A → dA<br>
A ← dA<br>
A ∨ dA
|}
|-
| f<sub>3</sub>
| g<sub>15</sub>
| 1 1 1 1
| (( ))
| True
| 1
|}
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====Old Versions====
====Old Versions====