Line 1: |
Line 1: |
| + | ==Logic of Relatives== |
| + | |
| + | <br> |
| + | |
| + | {| align="center" cellspacing="6" width="90%" |
| + | | align="center" | |
| + | <pre> |
| + | Table 3. Relational Composition |
| + | o---------o---------o---------o---------o |
| + | | # !1! | !1! | !1! | |
| + | o=========o=========o=========o=========o |
| + | | L # X | Y | | |
| + | o---------o---------o---------o---------o |
| + | | M # | Y | Z | |
| + | o---------o---------o---------o---------o |
| + | | L o M # X | | Z | |
| + | o---------o---------o---------o---------o |
| + | </pre> |
| + | |} |
| + | |
| + | <br> |
| + | |
| + | {| align="center" cellpadding="10" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center; width:60%" |
| + | |+ <math>\text{Table 3. Relational Composition}\!</math> |
| + | |- |
| + | | style="border-right:1px solid black; border-bottom:1px solid black; width:25%" | |
| + | | style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math> |
| + | | style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math> |
| + | | style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math> |
| + | |- |
| + | | style="border-right:1px solid black" | <math>L\!</math> |
| + | | <math>X\!</math> |
| + | | <math>Y\!</math> |
| + | | |
| + | |- |
| + | | style="border-right:1px solid black" | <math>M\!</math> |
| + | | |
| + | | <math>Y\!</math> |
| + | | <math>Z\!</math> |
| + | |- |
| + | | style="border-right:1px solid black" | <math>L \circ M</math> |
| + | | <math>X\!</math> |
| + | | |
| + | | <math>Z\!</math> |
| + | |} |
| + | |
| + | <br> |
| + | |
| + | {| align="center" cellspacing="6" width="90%" |
| + | | align="center" | |
| + | <pre> |
| + | Table 9. Composite of Triadic and Dyadic Relations |
| + | o---------o---------o---------o---------o---------o |
| + | | # !1! | !1! | !1! | !1! | |
| + | o=========o=========o=========o=========o=========o |
| + | | G # T | U | | V | |
| + | o---------o---------o---------o---------o---------o |
| + | | L # | U | W | | |
| + | o---------o---------o---------o---------o---------o |
| + | | G o L # T | | W | V | |
| + | o---------o---------o---------o---------o---------o |
| + | </pre> |
| + | |} |
| + | |
| + | <br> |
| + | |
| + | {| align="center" cellpadding="10" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center; width:75%" |
| + | |+ <math>\text{Table 9. Composite of Triadic and Dyadic Relations}\!</math> |
| + | |- |
| + | | style="border-right:1px solid black; border-bottom:1px solid black; width:20%" | |
| + | | style="border-bottom:1px solid black; width:20%" | <math>\mathit{1}\!</math> |
| + | | style="border-bottom:1px solid black; width:20%" | <math>\mathit{1}\!</math> |
| + | | style="border-bottom:1px solid black; width:20%" | <math>\mathit{1}\!</math> |
| + | | style="border-bottom:1px solid black; width:20%" | <math>\mathit{1}\!</math> |
| + | |- |
| + | | style="border-right:1px solid black" | <math>G\!</math> |
| + | | <math>T\!</math> |
| + | | <math>U\!</math> |
| + | | |
| + | | <math>V\!</math> |
| + | |- |
| + | | style="border-right:1px solid black" | <math>L\!</math> |
| + | | |
| + | | <math>U\!</math> |
| + | | <math>W\!</math> |
| + | | |
| + | |- |
| + | | style="border-right:1px solid black" | <math>G \circ L</math> |
| + | | <math>T\!</math> |
| + | | |
| + | | <math>W\!</math> |
| + | | <math>V\!</math> |
| + | |} |
| + | |
| + | <br> |
| + | |
| + | {| align="center" cellspacing="6" width="90%" |
| + | | align="center" | |
| + | <pre> |
| + | Table 13. Another Brand of Composition |
| + | o---------o---------o---------o---------o |
| + | | # !1! | !1! | !1! | |
| + | o=========o=========o=========o=========o |
| + | | G # X | Y | Z | |
| + | o---------o---------o---------o---------o |
| + | | T # | Y | Z | |
| + | o---------o---------o---------o---------o |
| + | | G o T # X | | Z | |
| + | o---------o---------o---------o---------o |
| + | </pre> |
| + | |} |
| + | |
| + | <br> |
| + | |
| + | {| align="center" cellpadding="10" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center; width:60%" |
| + | |+ <math>\text{Table 13. Another Brand of Composition}\!</math> |
| + | |- |
| + | | style="border-right:1px solid black; border-bottom:1px solid black; width:25%" | |
| + | | style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math> |
| + | | style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math> |
| + | | style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math> |
| + | |- |
| + | | style="border-right:1px solid black" | <math>G\!</math> |
| + | | <math>X\!</math> |
| + | | <math>Y\!</math> |
| + | | <math>Z\!</math> |
| + | |- |
| + | | style="border-right:1px solid black" | <math>T\!</math> |
| + | | |
| + | | <math>Y\!</math> |
| + | | <math>Z\!</math> |
| + | |- |
| + | | style="border-right:1px solid black" | <math>G \circ T</math> |
| + | | <math>X\!</math> |
| + | | |
| + | | <math>Z\!</math> |
| + | |} |
| + | |
| + | <br> |
| + | |
| + | {| align="center" cellspacing="6" width="90%" |
| + | | align="center" | |
| + | <pre> |
| + | Table 15. Conjunction Via Composition |
| + | o---------o---------o---------o---------o |
| + | | # !1! | !1! | !1! | |
| + | o=========o=========o=========o=========o |
| + | | L, # X | X | Y | |
| + | o---------o---------o---------o---------o |
| + | | S # | X | Y | |
| + | o---------o---------o---------o---------o |
| + | | L , S # X | | Y | |
| + | o---------o---------o---------o---------o |
| + | </pre> |
| + | |} |
| + | |
| + | <br> |
| + | |
| + | {| align="center" cellpadding="10" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center; width:60%" |
| + | |+ <math>\text{Table 15. Conjunction Via Composition}\!</math> |
| + | |- |
| + | | style="border-right:1px solid black; border-bottom:1px solid black; width:25%" | |
| + | | style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math> |
| + | | style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math> |
| + | | style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math> |
| + | |- |
| + | | style="border-right:1px solid black" | <math>L,\!</math> |
| + | | <math>X\!</math> |
| + | | <math>X\!</math> |
| + | | <math>Y\!</math> |
| + | |- |
| + | | style="border-right:1px solid black" | <math>S\!</math> |
| + | | |
| + | | <math>X\!</math> |
| + | | <math>Y\!</math> |
| + | |- |
| + | | style="border-right:1px solid black" | <math>L,\!S</math> |
| + | | <math>X\!</math> |
| + | | |
| + | | <math>Y\!</math> |
| + | |} |
| + | |
| + | <br> |
| + | |
| + | {| align="center" cellspacing="6" width="90%" |
| + | | align="center" | |
| + | <pre> |
| + | Table 18. Relational Composition P o Q |
| + | o---------o---------o---------o---------o |
| + | | # !1! | !1! | !1! | |
| + | o=========o=========o=========o=========o |
| + | | P # X | Y | | |
| + | o---------o---------o---------o---------o |
| + | | Q # | Y | Z | |
| + | o---------o---------o---------o---------o |
| + | | P o Q # X | | Z | |
| + | o---------o---------o---------o---------o |
| + | </pre> |
| + | |} |
| + | |
| + | <br> |
| + | |
| + | {| align="center" cellpadding="10" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center; width:60%" |
| + | |+ <math>\text{Table 18. Relational Composition}~ P \circ Q</math> |
| + | |- |
| + | | style="border-right:1px solid black; border-bottom:1px solid black; width:25%" | |
| + | | style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math> |
| + | | style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math> |
| + | | style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math> |
| + | |- |
| + | | style="border-right:1px solid black" | <math>P\!</math> |
| + | | <math>X\!</math> |
| + | | <math>Y\!</math> |
| + | | |
| + | |- |
| + | | style="border-right:1px solid black" | <math>Q\!</math> |
| + | | |
| + | | <math>Y\!</math> |
| + | | <math>Z\!</math> |
| + | |- |
| + | | style="border-right:1px solid black" | <math>P \circ Q</math> |
| + | | <math>X\!</math> |
| + | | |
| + | | <math>Z\!</math> |
| + | |} |
| + | |
| + | <br> |
| + | |
| + | {| align="center" cellspacing="6" width="90%" |
| + | | align="center" | |
| + | <pre> |
| + | Table 20. Arrow: J(L(u, v)) = K(Ju, Jv) |
| + | o---------o---------o---------o---------o |
| + | | # J | J | J | |
| + | o=========o=========o=========o=========o |
| + | | K # X | X | X | |
| + | o---------o---------o---------o---------o |
| + | | L # Y | Y | Y | |
| + | o---------o---------o---------o---------o |
| + | </pre> |
| + | |} |
| + | |
| + | <br> |
| + | |
| + | {| align="center" cellpadding="10" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center; width:60%" |
| + | |+ <math>\text{Table 20. Arrow Equation:}~~ J(L(u, v)) = K(Ju, Jv)</math> |
| + | |- |
| + | | style="border-right:1px solid black; border-bottom:1px solid black; width:25%" | |
| + | | style="border-bottom:1px solid black; width:25%" | <math>J\!</math> |
| + | | style="border-bottom:1px solid black; width:25%" | <math>J\!</math> |
| + | | style="border-bottom:1px solid black; width:25%" | <math>J\!</math> |
| + | |- |
| + | | style="border-right:1px solid black" | <math>K\!</math> |
| + | | <math>X\!</math> |
| + | | <math>X\!</math> |
| + | | <math>X\!</math> |
| + | |- |
| + | | style="border-right:1px solid black" | <math>L\!</math> |
| + | | <math>Y\!</math> |
| + | | <math>Y\!</math> |
| + | | <math>Y\!</math> |
| + | |} |
| + | |
| + | <br> |
| + | |
| ==Grammar Stuff== | | ==Grammar Stuff== |
| | | |
Line 150: |
Line 415: |
| <br> | | <br> |
| | | |
− | <pre>
| + | {| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:90%" |
− | Table 15. Boolean Functions on Zero Variables | + | |+ '''Table 15. Boolean Functions on Zero Variables''' |
− | o----------o----------o-------------------------------------------o----------o
| + | |- style="background:whitesmoke" |
− | | Constant | Function | F() | Function | | + | | width="14%" | <math>F\!</math> |
− | o----------o----------o-------------------------------------------o----------o
| + | | width="14%" | <math>F\!</math> |
− | | | | | | | + | | width="48%" | <math>F()\!</math> |
− | | %0% | F^0_0 | %0% | () | | + | | width="24%" | <math>F\!</math> |
− | | | | | | | + | |- |
− | | %1% | F^0_1 | %1% | (()) | | + | | <math>\underline{0}</math> |
− | | | | | |
| + | | <math>F_0^{(0)}\!</math> |
− | o----------o----------o-------------------------------------------o----------o
| + | | <math>\underline{0}</math> |
− | </pre> | + | | <math>(~)</math> |
| + | |- |
| + | | <math>\underline{1}</math> |
| + | | <math>F_1^{(0)}\!</math> |
| + | | <math>\underline{1}</math> |
| + | | <math>((~))</math> |
| + | |} |
| | | |
| <br> | | <br> |
| | | |
− | {| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:90%" | + | {| align="center" border="1" cellpadding="6" cellspacing="0" style="text-align:center; width:90%" |
| |+ '''Table 16. Boolean Functions on One Variable''' | | |+ '''Table 16. Boolean Functions on One Variable''' |
− | |- style="background:ghostwhite" | + | |- style="background:whitesmoke" |
− | | 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:whitesmoke" |
− | | width="20%" | | + | | width="14%" | |
− | | width="20%" | | + | | width="14%" | |
− | | 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%" | | + | | width="24%" | |
| |- | | |- |
| | <math>F_0^{(1)}\!</math> | | | <math>F_0^{(1)}\!</math> |
Line 183: |
Line 454: |
| | <math>\underline{0}</math> | | | <math>\underline{0}</math> |
| | <math>\underline{0}</math> | | | <math>\underline{0}</math> |
− | | <math>\underline{(} ~ \underline{)}</math> | + | | <math>(~)</math> |
| |- | | |- |
| | <math>F_1^{(1)}\!</math> | | | <math>F_1^{(1)}\!</math> |
Line 189: |
Line 460: |
| | <math>\underline{0}</math> | | | <math>\underline{0}</math> |
| | <math>\underline{1}</math> | | | <math>\underline{1}</math> |
− | | <math>\underline{(} x \underline{)}</math> | + | | <math>(x)\!</math> |
| |- | | |- |
| | <math>F_2^{(1)}\!</math> | | | <math>F_2^{(1)}\!</math> |
Line 201: |
Line 472: |
| | <math>\underline{1}</math> | | | <math>\underline{1}</math> |
| | <math>\underline{1}</math> | | | <math>\underline{1}</math> |
− | | <math>\underline{((} ~ \underline{))}</math> | + | | <math>((~))</math> |
| |} | | |} |
| | | |
| <br> | | <br> |
| | | |
− | <pre>
| + | {| align="center" border="1" cellpadding="4" cellspacing="0" style="text-align:center; width:90%" |
− | Table 17. Boolean Functions on Two Variables
| + | |+ '''Table 17. Boolean Functions on Two Variables''' |
− | o----------o----------o-------------------------------------------o----------o
| + | |- style="background:whitesmoke" |
− | | Function | Function | F(x, y) | Function |
| + | | width="14%" | <math>F\!</math> |
− | o----------o----------o----------o----------o----------o----------o----------o
| + | | width="14%" | <math>F\!</math> |
− | | | | %1%, %1% | %1%, %0% | %0%, %1% | %0%, %0% | |
| + | | colspan="4" | <math>F(x, y)\!</math> |
− | o----------o----------o----------o----------o----------o----------o----------o
| + | | width="24%" | <math>F\!</math> |
− | | | | | | | | |
| + | |- style="background:whitesmoke" |
− | | F^2_00 | F^2_0000 | %0% | %0% | %0% | %0% | () |
| + | | width="14%" | |
− | | | | | | | | |
| + | | width="14%" | |
− | | F^2_01 | F^2_0001 | %0% | %0% | %0% | %1% | (x)(y) |
| + | | width="12%" | <math>F(\underline{1}, \underline{1})</math> |
− | | | | | | | | |
| + | | width="12%" | <math>F(\underline{1}, \underline{0})</math> |
− | | F^2_02 | F^2_0010 | %0% | %0% | %1% | %0% | (x) y |
| + | | width="12%" | <math>F(\underline{0}, \underline{1})</math> |
− | | | | | | | | |
| + | | width="12%" | <math>F(\underline{0}, \underline{0})</math> |
− | | F^2_03 | F^2_0011 | %0% | %0% | %1% | %1% | (x) |
| + | | width="24%" | |
− | | | | | | | | |
| |
− | | F^2_04 | F^2_0100 | %0% | %1% | %0% | %0% | x (y) |
| |
− | | | | | | | | |
| |
− | | F^2_05 | F^2_0101 | %0% | %1% | %0% | %1% | (y) |
| |
− | | | | | | | | |
| |
− | | F^2_06 | F^2_0110 | %0% | %1% | %1% | %0% | (x, y) |
| |
− | | | | | | | | |
| |
− | | F^2_07 | F^2_0111 | %0% | %1% | %1% | %1% | (x y) |
| |
− | | | | | | | | |
| |
− | | F^2_08 | F^2_1000 | %1% | %0% | %0% | %0% | x y |
| |
− | | | | | | | | |
| |
− | | F^2_09 | F^2_1001 | %1% | %0% | %0% | %1% | ((x, y)) |
| |
− | | | | | | | | |
| |
− | | F^2_10 | F^2_1010 | %1% | %0% | %1% | %0% | y |
| |
− | | | | | | | | |
| |
− | | F^2_11 | F^2_1011 | %1% | %0% | %1% | %1% | (x (y)) |
| |
− | | | | | | | | |
| |
− | | F^2_12 | F^2_1100 | %1% | %1% | %0% | %0% | x |
| |
− | | | | | | | | |
| |
− | | F^2_13 | F^2_1101 | %1% | %1% | %0% | %1% | ((x) y) |
| |
− | | | | | | | | |
| |
− | | F^2_14 | F^2_1110 | %1% | %1% | %1% | %0% | ((x)(y)) |
| |
− | | | | | | | | |
| |
− | | F^2_15 | F^2_1111 | %1% | %1% | %1% | %1% | (()) |
| |
− | | | | | | | | |
| |
− | o----------o----------o----------o----------o----------o----------o----------o
| |
− | </pre>
| |
− | | |
− | <br>
| |
− | | |
− | {| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:96%" | |
− | |+ '''Table 7. Propositional Forms on Two Variables''' | |
− | |- style="background:ghostwhite" | |
− | | style="width:16%" | | |
− | <math>\begin{matrix}\mathcal{L}_1 \\ \mbox{Decimal}\end{matrix}</math> | |
− | | style="width:16%" | | |
− | <math>\begin{matrix}\mathcal{L}_2 \\ \mbox{Binary}\end{matrix}</math> | |
− | | style="width:16%" | | |
− | <math>\begin{matrix}\mathcal{L}_3 \\ \mbox{Vector}\end{matrix}</math> | |
− | | style="width:16%" | | |
− | <math>\begin{matrix}\mathcal{L}_4 \\ \mbox{Cactus}\end{matrix}</math> | |
− | | style="width:16%" | | |
− | <math>\begin{matrix}\mathcal{L}_5 \\ \mbox{English}\end{matrix}</math> | |
− | | style="width:16%" | | |
− | <math>\begin{matrix}\mathcal{L}_6 \\ \mbox{Ordinary}\end{matrix}</math> | |
− | |- style="background:ghostwhite" | |
− | | <math>~\!</math> | |
− | | align="right" | <math>x\colon\!</math> | |
− | | <math>1~1~0~0\!</math>
| |
− | | <math>~\!</math> | |
− | | <math>~\!</math> | |
− | | <math>~\!</math>
| |
| |- | | |- |
− | |- style="background:ghostwhite" | + | | <math>F_{0}^{(2)}\!</math> |
− | | <math>~\!</math> | + | | <math>F_{0000}^{(2)}\!</math> |
− | | align="right" | <math>y\colon\!</math>
| + | | <math>\underline{0}</math> |
− | | <math>1~0~1~0\!</math> | + | | <math>\underline{0}</math> |
− | | <math>~\!</math> | + | | <math>\underline{0}</math> |
− | | <math>~\!</math> | + | | <math>\underline{0}</math> |
− | | <math>~\!</math> | + | | <math>(~)</math> |
| |- | | |- |
− | | <math>f_{0}\!</math> | + | | <math>F_{1}^{(2)}\!</math> |
− | | <math>f_{0000}\!</math> | + | | <math>F_{0001}^{(2)}\!</math> |
− | | <math>0~0~0~0\!</math>
| + | | <math>\underline{0}</math> |
− | | <math>(~)\!</math>
| + | | <math>\underline{0}</math> |
− | | <math>\mbox{false}\!</math> | + | | <math>\underline{0}</math> |
− | | <math>0\!</math> | + | | <math>\underline{1}</math> |
− | |-
| |
− | | <math>f_{1}\!</math>
| |
− | | <math>f_{0001}\!</math> | |
− | | <math>0~0~0~1\!</math> | |
| | <math>(x)(y)\!</math> | | | <math>(x)(y)\!</math> |
− | | <math>\mbox{neither}\ x\ \mbox{nor}\ y\!</math>
| |
− | | <math>\lnot x \land \lnot y\!</math>
| |
| |- | | |- |
− | | <math>f_{2}\!</math> | + | | <math>F_{2}^{(2)}\!</math> |
− | | <math>f_{0010}\!</math> | + | | <math>F_{0010}^{(2)}\!</math> |
− | | <math>0~0~1~0\!</math> | + | | <math>\underline{0}</math> |
− | | <math>(x)\ y\!</math> | + | | <math>\underline{0}</math> |
− | | <math>y\ \mbox{without}\ x\!</math> | + | | <math>\underline{1}</math> |
− | | <math>\lnot x \land y\!</math> | + | | <math>\underline{0}</math> |
| + | | <math>(x) y\!</math> |
| |- | | |- |
− | | <math>f_{3}\!</math> | + | | <math>F_{3}^{(2)}\!</math> |
− | | <math>f_{0011}\!</math> | + | | <math>F_{0011}^{(2)}\!</math> |
− | | <math>0~0~1~1\!</math> | + | | <math>\underline{0}</math> |
| + | | <math>\underline{0}</math> |
| + | | <math>\underline{1}</math> |
| + | | <math>\underline{1}</math> |
| | <math>(x)\!</math> | | | <math>(x)\!</math> |
− | | <math>\mbox{not}\ x\!</math>
| |
− | | <math>\lnot x\!</math>
| |
| |- | | |- |
− | | <math>f_{4}\!</math> | + | | <math>F_{4}^{(2)}\!</math> |
− | | <math>f_{0100}\!</math> | + | | <math>F_{0100}^{(2)}\!</math> |
− | | <math>0~1~0~0\!</math> | + | | <math>\underline{0}</math> |
− | | <math>x\ (y)\!</math> | + | | <math>\underline{1}</math> |
− | | <math>x\ \mbox{without}\ y\!</math> | + | | <math>\underline{0}</math> |
− | | <math>x \land \lnot y\!</math> | + | | <math>\underline{0}</math> |
| + | | <math>x (y)\!</math> |
| |- | | |- |
− | | <math>f_{5}\!</math> | + | | <math>F_{5}^{(2)}\!</math> |
− | | <math>f_{0101}\!</math> | + | | <math>F_{0101}^{(2)}\!</math> |
− | | <math>0~1~0~1\!</math> | + | | <math>\underline{0}</math> |
| + | | <math>\underline{1}</math> |
| + | | <math>\underline{0}</math> |
| + | | <math>\underline{1}</math> |
| | <math>(y)\!</math> | | | <math>(y)\!</math> |
− | | <math>\mbox{not}\ y\!</math>
| |
− | | <math>\lnot y\!</math>
| |
| |- | | |- |
− | | <math>f_{6}\!</math> | + | | <math>F_{6}^{(2)}\!</math> |
− | | <math>f_{0110}\!</math> | + | | <math>F_{0110}^{(2)}\!</math> |
− | | <math>0~1~1~0\!</math> | + | | <math>\underline{0}</math> |
| + | | <math>\underline{1}</math> |
| + | | <math>\underline{1}</math> |
| + | | <math>\underline{0}</math> |
| | <math>(x, y)\!</math> | | | <math>(x, y)\!</math> |
− | | <math>x\ \mbox{not equal to}\ y\!</math>
| |
− | | <math>x \ne y\!</math>
| |
| |- | | |- |
− | | <math>f_{7}\!</math> | + | | <math>F_{7}^{(2)}\!</math> |
− | | <math>f_{0111}\!</math> | + | | <math>F_{0111}^{(2)}\!</math> |
− | | <math>0~1~1~1\!</math> | + | | <math>\underline{0}</math> |
− | | <math>(x\ y)\!</math> | + | | <math>\underline{1}</math> |
− | | <math>\mbox{not both}\ x\ \mbox{and}\ y\!</math> | + | | <math>\underline{1}</math> |
− | | <math>\lnot x \lor \lnot y\!</math> | + | | <math>\underline{1}</math> |
| + | | <math>(x y)\!</math> |
| |- | | |- |
− | | <math>f_{8}\!</math> | + | | <math>F_{8}^{(2)}\!</math> |
− | | <math>f_{1000}\!</math> | + | | <math>F_{1000}^{(2)}\!</math> |
− | | <math>1~0~0~0\!</math> | + | | <math>\underline{1}</math> |
− | | <math>x\ y\!</math> | + | | <math>\underline{0}</math> |
− | | <math>x\ \mbox{and}\ y\!</math> | + | | <math>\underline{0}</math> |
− | | <math>x \land y\!</math> | + | | <math>\underline{0}</math> |
| + | | <math>x y\!</math> |
| |- | | |- |
− | | <math>f_{9}\!</math> | + | | <math>F_{9}^{(2)}\!</math> |
− | | <math>f_{1001}\!</math> | + | | <math>F_{1001}^{(2)}\!</math> |
− | | <math>1~0~0~1\!</math> | + | | <math>\underline{1}</math> |
| + | | <math>\underline{0}</math> |
| + | | <math>\underline{0}</math> |
| + | | <math>\underline{1}</math> |
| | <math>((x, y))\!</math> | | | <math>((x, y))\!</math> |
− | | <math>x\ \mbox{equal to}\ y\!</math>
| |
− | | <math>x = y\!</math>
| |
| |- | | |- |
− | | <math>f_{10}\!</math> | + | | <math>F_{10}^{(2)}\!</math> |
− | | <math>f_{1010}\!</math> | + | | <math>F_{1010}^{(2)}\!</math> |
− | | <math>1~0~1~0\!</math> | + | | <math>\underline{1}</math> |
− | | <math>y\!</math> | + | | <math>\underline{0}</math> |
− | | <math>y\!</math> | + | | <math>\underline{1}</math> |
| + | | <math>\underline{0}</math> |
| | <math>y\!</math> | | | <math>y\!</math> |
| |- | | |- |
− | | <math>f_{11}\!</math> | + | | <math>F_{11}^{(2)}\!</math> |
− | | <math>f_{1011}\!</math> | + | | <math>F_{1011}^{(2)}\!</math> |
− | | <math>1~0~1~1\!</math> | + | | <math>\underline{1}</math> |
− | | <math>(x\ (y))\!</math> | + | | <math>\underline{0}</math> |
− | | <math>\mbox{not}\ x\ \mbox{without}\ y\!</math> | + | | <math>\underline{1}</math> |
− | | <math>x \Rightarrow y\!</math> | + | | <math>\underline{1}</math> |
| + | | <math>(x (y))\!</math> |
| |- | | |- |
− | | <math>f_{12}\!</math> | + | | <math>F_{12}^{(2)}\!</math> |
− | | <math>f_{1100}\!</math> | + | | <math>F_{1100}^{(2)}\!</math> |
− | | <math>1~1~0~0\!</math> | + | | <math>\underline{1}</math> |
− | | <math>x\!</math> | + | | <math>\underline{1}</math> |
− | | <math>x\!</math> | + | | <math>\underline{0}</math> |
| + | | <math>\underline{0}</math> |
| | <math>x\!</math> | | | <math>x\!</math> |
| |- | | |- |
− | | <math>f_{13}\!</math> | + | | <math>F_{13}^{(2)}\!</math> |
− | | <math>f_{1101}\!</math> | + | | <math>F_{1101}^{(2)}\!</math> |
− | | <math>1~1~0~1\!</math> | + | | <math>\underline{1}</math> |
− | | <math>((x)\ y)\!</math> | + | | <math>\underline{1}</math> |
− | | <math>\mbox{not}\ y\ \mbox{without}\ x\!</math> | + | | <math>\underline{0}</math> |
− | | <math>x \Leftarrow y\!</math> | + | | <math>\underline{1}</math> |
| + | | <math>((x)y)\!</math> |
| |- | | |- |
− | | <math>f_{14}\!</math> | + | | <math>F_{14}^{(2)}\!</math> |
− | | <math>f_{1110}\!</math> | + | | <math>F_{1110}^{(2)}\!</math> |
− | | <math>1~1~1~0\!</math> | + | | <math>\underline{1}</math> |
| + | | <math>\underline{1}</math> |
| + | | <math>\underline{1}</math> |
| + | | <math>\underline{0}</math> |
| | <math>((x)(y))\!</math> | | | <math>((x)(y))\!</math> |
− | | <math>x\ \mbox{or}\ y\!</math>
| |
− | | <math>x \lor y\!</math>
| |
| |- | | |- |
− | | <math>f_{15}\!</math> | + | | <math>F_{15}^{(2)}\!</math> |
− | | <math>f_{1111}\!</math> | + | | <math>F_{1111}^{(2)}\!</math> |
− | | <math>1~1~1~1\!</math> | + | | <math>\underline{1}</math> |
− | | <math>((~))\!</math> | + | | <math>\underline{1}</math> |
− | | <math>\mbox{true}\!</math> | + | | <math>\underline{1}</math> |
− | | <math>1\!</math> | + | | <math>\underline{1}</math> |
| + | | <math>((~))</math> |
| |} | | |} |
| | | |