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| <math>\beta_i f = \Upsilon \langle f, f_i \rangle = \Upsilon \langle f \Rightarrow f_i \rangle.</math>
| <math>\beta_i f = \Upsilon \langle f, f_i \rangle = \Upsilon \langle f \Rightarrow f_i \rangle.</math>
|}
|}
====Table 1====
The values of the sixteen <math>\alpha_i\!</math> on each of the sixteen boolean functions <math>f : \mathbb{B}^2 \to \mathbb{B}</math> are shown in Table 1. Expressed in terms of the implication ordering on the sixteen functions, <math>\alpha_i f = 1\!</math> says that <math>f\!</math> is ''above or identical to'' <math>f_i\!</math> in the implication lattice, that is, <math>\ge f_i\!</math> in the implication ordering.
The values of the sixteen <math>\alpha_i\!</math> on each of the sixteen boolean functions <math>f : \mathbb{B}^2 \to \mathbb{B}</math> are shown in Table 1. Expressed in terms of the implication ordering on the sixteen functions, <math>\alpha_i f = 1\!</math> says that <math>f\!</math> is ''above or identical to'' <math>f_i\!</math> in the implication lattice, that is, <math>\ge f_i\!</math> in the implication ordering.
| style="background:black; color:white" | 1
| style="background:black; color:white" | 1
|}<br>
|}<br>
====Table 2====
The values of the sixteen <math>\beta_i\!</math> on each of the sixteen boolean functions <math>f : \mathbb{B}^2 \to \mathbb{B}</math> are shown in Table 2. Expressed in terms of the implication ordering on the sixteen functions, <math>\beta_i f = 1\!</math> says that <math>f\!</math> is ''below or identical to'' <math>f_i\!</math> in the implication lattice, that is, <math>\le f_i\!</math> in the implication ordering.
The values of the sixteen <math>\beta_i\!</math> on each of the sixteen boolean functions <math>f : \mathbb{B}^2 \to \mathbb{B}</math> are shown in Table 2. Expressed in terms of the implication ordering on the sixteen functions, <math>\beta_i f = 1\!</math> says that <math>f\!</math> is ''below or identical to'' <math>f_i\!</math> in the implication lattice, that is, <math>\le f_i\!</math> in the implication ordering.
| style="background:black; color:white" | 1
| style="background:black; color:white" | 1
|}<br>
|}<br>
====Table 3====
{| align="center" border="1" cellpadding="2" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
{| align="center" border="1" cellpadding="2" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
| 0000
| 0000
| <math>(~)</math>
| <math>(~)</math>
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
|-
|-
| <math>f_1</math>
| <math>f_1</math>
| 0001
| 0001
| <math>(u)(v)\!</math>
| <math>(u)(v)\!</math>
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
|-
|-
| <math>f_2</math>
| <math>f_2</math>
| 0010
| 0010
| <math>(u) v\!</math>
| <math>(u) v\!</math>
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
|-
|-
| <math>f_3</math>
| <math>f_3</math>
| 0011
| 0011
| <math>(u)\!</math>
| <math>(u)\!</math>
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
|-
|-
| <math>f_4</math>
| <math>f_4</math>
| 0100
| 0100
| <math>u (v)\!</math>
| <math>u (v)\!</math>
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|-
|-
| <math>f_5</math>
| <math>f_5</math>
| 0101
| 0101
| <math>(v)\!</math>
| <math>(v)\!</math>
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|-
|-
| <math>f_6</math>
| <math>f_6</math>
| 0110
| 0110
| <math>(u, v)\!</math>
| <math>(u, v)\!</math>
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|-
|-
| <math>f_7</math>
| <math>f_7</math>
| 0111
| 0111
| <math>(u v)\!</math>
| <math>(u v)\!</math>
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|-
|-
| <math>f_8</math>
| <math>f_8</math>
| 1000
| 1000
| <math>u v\!</math>
| <math>u v\!</math>
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|-
|-
| <math>f_9</math>
| <math>f_9</math>
| 1001
| 1001
| <math>((u, v))\!</math>
| <math>((u, v))\!</math>
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|-
|-
| <math>f_{10}</math>
| <math>f_{10}</math>
| 1010
| 1010
| <math>v\!</math>
| <math>v\!</math>
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|-
|-
| <math>f_{11}</math>
| <math>f_{11}</math>
| 1011
| 1011
| <math>(u (v))\!</math>
| <math>(u (v))\!</math>
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|-
|-
| <math>f_{12}</math>
| <math>f_{12}</math>
| 1100
| 1100
| <math>u\!</math>
| <math>u\!</math>
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|-
|-
| <math>f_{13}</math>
| <math>f_{13}</math>
| 1101
| 1101
| <math>((u) v)\!</math>
| <math>((u) v)\!</math>
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|-
|-
| <math>f_{14}</math>
| <math>f_{14}</math>
| 1110
| 1110
| <math>((u)(v))\!</math>
| <math>((u)(v))\!</math>
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|-
|-
| <math>f_{15}</math>
| <math>f_{15}</math>
| 1111
| 1111
| <math>((~))</math>
| <math>((~))</math>
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|}<br>
|}<br>
====Table 4====
{| align="center" border="1" cellpadding="2" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
{| align="center" border="1" cellpadding="2" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
| 0000
| 0000
| <math>(~)</math>
| <math>(~)</math>
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
|-
|-
| <math>f_1</math>
| <math>f_1</math>
| 0001
| 0001
| <math>(u)(v)\!</math>
| <math>(u)(v)\!</math>
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
|-
|-
| <math>f_2</math>
| <math>f_2</math>
| 0010
| 0010
| <math>(u) v\!</math>
| <math>(u) v\!</math>
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
|-
|-
| <math>f_4</math>
| <math>f_4</math>
| 0100
| 0100
| <math>u (v)\!</math>
| <math>u (v)\!</math>
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|-
|-
| <math>f_8</math>
| <math>f_8</math>
| 1000
| 1000
| <math>u v\!</math>
| <math>u v\!</math>
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|-
|-
| <math>f_3</math>
| <math>f_3</math>
| 0011
| 0011
| <math>(u)\!</math>
| <math>(u)\!</math>
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
|-
|-
| <math>f_{12}</math>
| <math>f_{12}</math>
| 1100
| 1100
| <math>u\!</math>
| <math>u\!</math>
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|-
|-
| <math>f_6</math>
| <math>f_6</math>
| 0110
| 0110
| <math>(u, v)\!</math>
| <math>(u, v)\!</math>
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|-
|-
| <math>f_9</math>
| <math>f_9</math>
| 1001
| 1001
| <math>((u, v))\!</math>
| <math>((u, v))\!</math>
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|-
|-
| <math>f_5</math>
| <math>f_5</math>
| 0101
| 0101
| <math>(v)\!</math>
| <math>(v)\!</math>
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|-
|-
| <math>f_{10}</math>
| <math>f_{10}</math>
| 1010
| 1010
| <math>v\!</math>
| <math>v\!</math>
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|-
|-
| <math>f_7</math>
| <math>f_7</math>
| 0111
| 0111
| <math>(u v)\!</math>
| <math>(u v)\!</math>
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|-
|-
| <math>f_{11}</math>
| <math>f_{11}</math>
| 1011
| 1011
| <math>(u (v))\!</math>
| <math>(u (v))\!</math>
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|-
|-
| <math>f_{13}</math>
| <math>f_{13}</math>
| 1101
| 1101
| <math>((u) v)\!</math>
| <math>((u) v)\!</math>
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|-
|-
| <math>f_{14}</math>
| <math>f_{14}</math>
| 1110
| 1110
| <math>((u)(v))\!</math>
| <math>((u)(v))\!</math>
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|-
|-
| <math>f_{15}</math>
| <math>f_{15}</math>
| 1111
| 1111
| <math>((~))</math>
| <math>((~))</math>
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
|
| style="background:white; color:black" | 0
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
| 1
| style="background:black; color:white" | 1
|}<br>
|}<br>
====Table 5====
{| align="center" border="1" cellpadding="2" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
{| align="center" border="1" cellpadding="2" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
