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MyWikiBiz, Author Your Legacy — Thursday November 07, 2024
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→‎Truth tables: HTML → LaTeX
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==Truth tables==
 
==Truth tables==
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Table 1 is a [[truth table]] for the sixteen boolean functions of type f&nbsp;:&nbsp;'''B'''<sup>3</sup>&nbsp;&rarr;&nbsp;'''B''', each of which is either a boundary of a point in '''B'''<sup>3</sup> or the complement of such a boundary.
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Table&nbsp;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.
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{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:#e6e6ff; font-weight:bold; text-align:center; width:80%"
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{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:whitesmoke; font-weight:bold; text-align:center; width:80%"
 
|+ Table 1.  Logical Boundaries and Their Complements
 
|+ Table 1.  Logical Boundaries and Their Complements
| width="20%" | L<sub>1</sub>
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| width="20%" | <math>\mathcal{L}_1</math>
| width="20%" | L<sub>2</sub>
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| width="20%" | <math>\mathcal{L}_2</math>
| width="20%" | L<sub>3</sub>
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| width="20%" | <math>\mathcal{L}_3</math>
| width="20%" | L<sub>4</sub>
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| width="20%" | <math>\mathcal{L}_4</math>
 
|-
 
|-
 
| Decimal
 
| Decimal
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|-
 
|-
 
| &nbsp;
 
| &nbsp;
| align="right" | p =
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| align="right" | <math>p =\!</math>
 
| 1 1 1 1 0 0 0 0
 
| 1 1 1 1 0 0 0 0
 
| &nbsp;
 
| &nbsp;
 
|-
 
|-
 
| &nbsp;
 
| &nbsp;
| align="right" | q =
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| align="right" | <math>q =\!</math>
 
| 1 1 0 0 1 1 0 0
 
| 1 1 0 0 1 1 0 0
 
| &nbsp;
 
| &nbsp;
 
|-
 
|-
 
| &nbsp;
 
| &nbsp;
| align="right" | r =
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| align="right" | <math>r =\!</math>
 
| 1 0 1 0 1 0 1 0
 
| 1 0 1 0 1 0 1 0
 
| &nbsp;
 
| &nbsp;
 
|}
 
|}
{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:ghostwhite; font-weight:bold; text-align:center; width:80%"
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{| 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%" | f<sub>104</sub>
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