12,140
edits
Changes
→Truth tables: HTML → LaTeX
==Truth tables==
==Truth tables==
Table 1 is a [[truth table]] for the sixteen boolean functions of type <math>f : \mathbb{B}^3 \to \mathbb{B},</math> each of which is either a boundary of a point in <math>\mathbb{B}^3</math> or the complement of such a boundary.
Table 1 is a [[truth table]] for the sixteen boolean functions of type <math>f : \mathbb{B}^3 \to \mathbb{B}</math> whose fibers of 1 are either the boundaries of points in <math>\mathbb{B}^3</math> or the complements of those boundaries.
{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:whitesmoke; font-weight:bold; text-align:center; width:80%"
{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:whitesmoke; font-weight:bold; text-align:center; width:80%"
{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:ghostwhite; font-weight:bold; text-align:center; width:80%"
{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:ghostwhite; font-weight:bold; text-align:center; width:80%"
|-
|-
| width="20%" | f<sub>104</sub>
| width="20%" | <math>f_{104}</math>
| width="20%" | f<sub>01101000</sub>
| width="20%" | <math>f_{01101000}</math>
| width="20%" | 0 1 1 0 1 0 0 0
| width="20%" | 0 1 1 0 1 0 0 0
| width="20%" | ( p , q , r )
| width="20%" | <math>( p , q , r )</math>
|-
|-
| f<sub>148</sub> || f<sub>10010100</sub> || 1 0 0 1 0 1 0 0 || ( p , q , (r))
| <math>f_{148}</math>
| <math>f_{10010100}</math>
| 1 0 0 1 0 1 0 0
| <math>( p , q , (r))</math>
|-
|-
| f<sub>146</sub> || f<sub>10010010</sub> || 1 0 0 1 0 0 1 0 || ( p , (q), r )
| <math>f_{146}</math>
| <math>f_{10010010}</math>
| 1 0 0 1 0 0 1 0
| <math>( p , (q), r )</math>
|-
|-
| f<sub>97</sub> || f<sub>01100001</sub> || 0 1 1 0 0 0 0 1 || ( p , (q), (r))
| <math>f_{97}</math>
| <math>f_{01100001}</math>
| 0 1 1 0 0 0 0 1
| <math>( p , (q), (r))</math>
|-
|-
| f<sub>134</sub> || f<sub>10000110</sub> || 1 0 0 0 0 1 1 0 || ((p), q , r )
| <math>f_{134}</math>
| <math>f_{10000110}</math>
| 1 0 0 0 0 1 1 0
| <math>((p), q , r )</math>
|-
|-
| f<sub>73</sub> || f<sub>01001001</sub> || 0 1 0 0 1 0 0 1 || ((p), q , (r))
| <math>f_{73}</math>
| <math>f_{01001001}</math>
| 0 1 0 0 1 0 0 1
| <math>((p), q , (r))</math>
|-
|-
| f<sub>41</sub> || f<sub>00101001</sub> || 0 0 1 0 1 0 0 1 || ((p), (q), r )
| <math>f_{41}</math>
| <math>f_{00101001}</math>
| 0 0 1 0 1 0 0 1
| <math>((p), (q), r )</math>
|-
|-
| f<sub>22</sub> || f<sub>00010110</sub> || 0 0 0 1 0 1 1 0 || ((p), (q), (r))
| <math>f_{22}</math>
| <math>f_{00010110}</math>
| 0 0 0 1 0 1 1 0
| <math>((p), (q), (r))</math>
|}
|}
{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:ghostwhite; font-weight:bold; text-align:center; width:80%"
{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:ghostwhite; font-weight:bold; text-align:center; width:80%"
|-
|-
| width="20%" | f<sub>233</sub>
| width="20%" | <math>f_{233}</math>
| width="20%" | f<sub>11101001</sub>
| width="20%" | <math>f_{11101001}</math>
| width="20%" | 1 1 1 0 1 0 0 1
| width="20%" | 1 1 1 0 1 0 0 1
| width="20%" | (((p), (q), (r)))
| width="20%" | <math>(((p), (q), (r)))</math>
|-
|-
| f<sub>214</sub> || f<sub>11010110</sub> || 1 1 0 1 0 1 1 0 || (((p), (q), r ))
| <math>f_{214}</math>
| <math>f_{11010110}</math>
| 1 1 0 1 0 1 1 0
| <math>(((p), (q), r ))</math>
|-
|-
| f<sub>182</sub> || f<sub>10110110</sub> || 1 0 1 1 0 1 1 0 || (((p), q , (r)))
| <math>f_{182}</math>
| <math>f_{10110110}</math>
| 1 0 1 1 0 1 1 0
| <math>(((p), q , (r)))</math>
|-
|-
| f<sub>121</sub> || f<sub>01111001</sub> || 0 1 1 1 1 0 0 1 || (((p), q , r ))
| <math>f_{121}</math>
| <math>f_{01111001}</math>
| 0 1 1 1 1 0 0 1
| <math>(((p), q , r ))</math>
|-
|-
| f<sub>158</sub> || f<sub>10011110</sub> || 1 0 0 1 1 1 1 0 || (( p , (q), (r)))
| <math>f_{158}</math>
| <math>f_{10011110}</math>
| 1 0 0 1 1 1 1 0
| <math>(( p , (q), (r)))</math>
|-
|-
| f<sub>109</sub> || f<sub>01101101</sub> || 0 1 1 0 1 1 0 1 || (( p , (q), r ))
| <math>f_{109}</math>
| <math>f_{01101101}</math>
| 0 1 1 0 1 1 0 1
| <math>(( p , (q), r ))</math>
|-
|-
| f<sub>107</sub> || f<sub>01101011</sub> || 0 1 1 0 1 0 1 1 || (( p , q , (r)))
| <math>f_{107}</math>
| <math>f_{01101011}</math>
| 0 1 1 0 1 0 1 1
| <math>(( p , q , (r)))</math>
|-
|-
| f<sub>151</sub> || f<sub>10010111</sub> || 1 0 0 1 0 1 1 1 || (( p , q , r ))
| <math>f_{151}</math>
| <math>f_{10010111}</math>
| 1 0 0 1 0 1 1 1
| <math>(( p , q , r ))</math>
|}
|}
<br>
<br>