Changes

A boolean function <math>F^{(0)}\!</math> on <math>0\!</math> variables is just an element of the boolean domain <math>\underline\mathbb{B} = \{ \underline{0}, \underline{1} \}.</math>  Table&nbsp;15 shows several different ways of referring to these elements, just for the sake of consistency using the same format that will be used in subsequent Tables, no matter how degenerate it tends to appear in the initial case.

A boolean function <math>F^{(0)}\!</math> on <math>0\!</math> variables is just an element of the boolean domain <math>\underline\mathbb{B} = \{ \underline{0}, \underline{1} \}.</math>  Table&nbsp;15 shows several different ways of referring to these elements, just for the sake of consistency using the same format that will be used in subsequent Tables, no matter how degenerate it tends to appear in the initial case.

<pre>

<br>

Table 15.  Boolean Functions on Zero Variables

 

o----------o----------o-------------------------------------------o----------o

| Constant | Function |                    F()                    | Function |

|+ '''Table 15.  Boolean Functions on Zero Variables'''

|- style="background:ghostwhite"

|         |         |                                           |         |

| width="14%" | <math>F\!</math>

| %0%      | F^0_0    |                   %0%                    |   ()   |

| width="14%" | <math>F\!</math>

|         |          |                                          |          |

| width="48%" | <math>F()\!</math>

| %1%      | F^0_1    |                   %1%                    |   (())   |

| width="24%" | <math>F\!</math>

|         |          |                                          |          |

|-

| <math>\underline{0}</math>

</pre>

| <math>F_0^{(0)}\!</math>

| <math>\underline{0}</math>

| <math>\underline{(} ~ \underline{)}</math>

|-

| <math>\underline{1}</math>

| <math>F_1^{(0)}\!</math>

| <math>\underline{1}</math>

| <math>\underline{((} ~ \underline{))}</math>

|}

 

<br>

Column&nbsp;1 lists each boolean element or boolean function under its ordinary constant name or under a succinct nickname, respectively.

Column&nbsp;1 lists each boolean element or boolean function under its ordinary constant name or under a succinct nickname, respectively.

|+ '''Table 16.  Boolean Functions on One Variable'''

|+ '''Table 16.  Boolean Functions on One Variable'''

|- style="background:ghostwhite"

|- style="background:ghostwhite"

| width="20%" | <math>F\!</math>

| width="14%" | <math>F\!</math>

| width="20%" | <math>F\!</math>

| width="14%" | <math>F\!</math>

| colspan="2" | <math>F(x)\!</math>

| colspan="2" | <math>F(x)\!</math>

| width="20%" | <math>F\!</math>

| width="24%" | <math>F\!</math>

|- style="background:ghostwhite"

|- style="background:ghostwhite"

| width="20%" | &nbsp;

| width="14%" | &nbsp;

| width="20%" | &nbsp;

| width="14%" | &nbsp;

| width="20%" | <math>F(\underline{1})</math>

| width="24%" | <math>F(\underline{1})</math>

| width="20%" | <math>F(\underline{0})</math>

| width="24%" | <math>F(\underline{0})</math>

| width="20%" | &nbsp;

| width="24%" | &nbsp;

|-

|-

| <math>F_0^{(1)}\!</math>

| <math>F_0^{(1)}\!</math>