Difference between revisions of "User:Jon Awbrey/MNO"

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| 1 0 0 1 0 1 1 1
 
| <math>(( p , q , r ))\!</math>
 
| <math>(( p , q , r ))\!</math>
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|}
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<br>
 +
 +
==Work Area==
 +
 +
<br>
 +
 +
{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:#f0f0ff; font-weight:bold; text-align:center; width:80%"
 +
|+ <math>\text{Table 1.}~~\text{Logical Boundaries and Their Complements}</math>
 +
| width="20%" | <math>\mathcal{L}_1</math>
 +
| width="20%" | <math>\mathcal{L}_2</math>
 +
| width="20%" | <math>\mathcal{L}_3</math>
 +
| width="20%" | <math>\mathcal{L}_4</math>
 +
|-
 +
| Decimal
 +
| Binary
 +
| Sequential
 +
| Parenthetical
 +
|-
 +
| &nbsp;
 +
| align="right" | <math>p =\!</math>
 +
| 1 1 1 1 0 0 0 0
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| &nbsp;
 +
|-
 +
| &nbsp;
 +
| align="right" | <math>q =\!</math>
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| 1 1 0 0 1 1 0 0
 +
| &nbsp;
 +
|-
 +
| &nbsp;
 +
| align="right" | <math>r =\!</math>
 +
| 1 0 1 0 1 0 1 0
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| &nbsp;
 +
|}
 +
{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:ghostwhite; font-weight:bold; text-align:center; width:80%"
 +
|-
 +
| width="20%" | <math>f_{104}\!</math>
 +
| width="20%" | <math>f_{01101000}\!</math>
 +
| width="20%" | 0 1 1 0 1 0 0 0
 +
| width="20%" | <math>( p , q , r )\!</math>
 +
|-
 +
| <math>f_{148}\!</math>
 +
| <math>f_{10010100}\!</math>
 +
| 1 0 0 1 0 1 0 0
 +
| <math>( p , q , (r))\!</math>
 +
|-
 +
| <math>f_{146}\!</math>
 +
| <math>f_{10010010}\!</math>
 +
| 1 0 0 1 0 0 1 0
 +
| <math>( p , (q), r )\!</math>
 +
|-
 +
| <math>f_{97}\!</math>
 +
| <math>f_{01100001}\!</math>
 +
| 0 1 1 0 0 0 0 1
 +
| <math>( p , (q), (r))\!</math>
 +
|-
 +
| <math>f_{134}\!</math>
 +
| <math>f_{10000110}\!</math>
 +
| 1 0 0 0 0 1 1 0
 +
| <math>((p), q , r )\!</math>
 +
|-
 +
| <math>f_{73}\!</math>
 +
| <math>f_{01001001}\!</math>
 +
| 0 1 0 0 1 0 0 1
 +
| <math>((p), q , (r))\!</math>
 +
|-
 +
| <math>f_{41}\!</math>
 +
| <math>f_{00101001}\!</math>
 +
| 0 0 1 0 1 0 0 1
 +
| <math>((p), (q), r )\!</math>
 +
|-
 +
| <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%"
 +
|-
 +
| width="20%" | <math>f_{233}\!</math>
 +
| width="20%" | <math>f_{11101001}\!</math>
 +
| width="20%" | 1 1 1 0 1 0 0 1
 +
| width="20%" | <math>(((p), (q), (r)))\!</math>
 +
|-
 +
| <math>f_{214}\!</math>
 +
| <math>f_{11010110}\!</math>
 +
| 1 1 0 1 0 1 1 0
 +
| <math>(((p), (q), r ))\!</math>
 +
|-
 +
| <math>f_{182}\!</math>
 +
| <math>f_{10110110}\!</math>
 +
| 1 0 1 1 0 1 1 0
 +
| <math>(((p), q , (r)))\!</math>
 +
|-
 +
| <math>f_{121}\!</math>
 +
| <math>f_{01111001}\!</math>
 +
| 0 1 1 1 1 0 0 1
 +
| <math>(((p), q , r ))\!</math>
 +
|-
 +
| <math>f_{158}\!</math>
 +
| <math>f_{10011110}\!</math>
 +
| 1 0 0 1 1 1 1 0
 +
| <math>(( p , (q), (r)))\!</math>
 +
|-
 +
| <math>f_{109}\!</math>
 +
| <math>f_{01101101}\!</math>
 +
| 0 1 1 0 1 1 0 1
 +
| <math>(( p , (q), r ))\!</math>
 +
|-
 +
| <math>f_{107}\!</math>
 +
| <math>f_{01101011}\!</math>
 +
| 0 1 1 0 1 0 1 1
 +
| <math>(( p , q , (r)))\!</math>
 +
|-
 +
| <math>f_{151}\!</math>
 +
| <math>f_{10010111}\!</math>
 +
| 1 0 0 1 0 1 1 1
 +
| <math>(( p , q , r ))\!</math>
 +
|}
 +
 +
<br>
 +
 +
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:90%"
 +
|+ <math>\text{Table A1.}~~\text{Propositional Forms on Two Variables}</math>
 +
|- style="background:#f0f0ff"
 +
| width="15%" |
 +
<p><math>\mathcal{L}_1</math></p>
 +
<p><math>\text{Decimal}</math></p>
 +
| width="15%" |
 +
<p><math>\mathcal{L}_2</math></p>
 +
<p><math>\text{Binary}</math></p>
 +
| width="15%" |
 +
<p><math>\mathcal{L}_3</math></p>
 +
<p><math>\text{Vector}</math></p>
 +
| width="15%" |
 +
<p><math>\mathcal{L}_4</math></p>
 +
<p><math>\text{Cactus}</math></p>
 +
| width="25%" |
 +
<p><math>\mathcal{L}_5</math></p>
 +
<p><math>\text{English}</math></p>
 +
| width="15%" |
 +
<p><math>\mathcal{L}_6</math></p>
 +
<p><math>\text{Ordinary}</math></p>
 +
|- style="background:#f0f0ff"
 +
| &nbsp;
 +
| align="right" | <math>p\colon\!</math>
 +
| <math>1~1~0~0\!</math>
 +
| &nbsp;
 +
| &nbsp;
 +
| &nbsp;
 +
|- style="background:#f0f0ff"
 +
| &nbsp;
 +
| align="right" | <math>q\colon\!</math>
 +
| <math>1~0~1~0\!</math>
 +
| &nbsp;
 +
| &nbsp;
 +
| &nbsp;
 +
|-
 +
|
 +
<math>\begin{matrix}
 +
f_0
 +
\\[4pt]
 +
f_1
 +
\\[4pt]
 +
f_2
 +
\\[4pt]
 +
f_3
 +
\\[4pt]
 +
f_4
 +
\\[4pt]
 +
f_5
 +
\\[4pt]
 +
f_6
 +
\\[4pt]
 +
f_7
 +
\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
f_{0000}
 +
\\[4pt]
 +
f_{0001}
 +
\\[4pt]
 +
f_{0010}
 +
\\[4pt]
 +
f_{0011}
 +
\\[4pt]
 +
f_{0100}
 +
\\[4pt]
 +
f_{0101}
 +
\\[4pt]
 +
f_{0110}
 +
\\[4pt]
 +
f_{0111}
 +
\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
0~0~0~0
 +
\\[4pt]
 +
0~0~0~1
 +
\\[4pt]
 +
0~0~1~0
 +
\\[4pt]
 +
0~0~1~1
 +
\\[4pt]
 +
0~1~0~0
 +
\\[4pt]
 +
0~1~0~1
 +
\\[4pt]
 +
0~1~1~0
 +
\\[4pt]
 +
0~1~1~1
 +
\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
(~)
 +
\\[4pt]
 +
(p)(q)
 +
\\[4pt]
 +
(p)~q~
 +
\\[4pt]
 +
(p)~~~
 +
\\[4pt]
 +
~p~(q)
 +
\\[4pt]
 +
~~~(q)
 +
\\[4pt]
 +
(p,~q)
 +
\\[4pt]
 +
(p~~q)
 +
\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
\text{false}
 +
\\[4pt]
 +
\text{neither}~ p ~\text{nor}~ q
 +
\\[4pt]
 +
q ~\text{without}~ p
 +
\\[4pt]
 +
\text{not}~ p
 +
\\[4pt]
 +
p ~\text{without}~ q
 +
\\[4pt]
 +
\text{not}~ q
 +
\\[4pt]
 +
p ~\text{not equal to}~ q
 +
\\[4pt]
 +
\text{not both}~ p ~\text{and}~ q
 +
\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
0
 +
\\[4pt]
 +
\lnot p \land \lnot q
 +
\\[4pt]
 +
\lnot p \land q
 +
\\[4pt]
 +
\lnot p
 +
\\[4pt]
 +
p \land \lnot q
 +
\\[4pt]
 +
\lnot q
 +
\\[4pt]
 +
p \ne q
 +
\\[4pt]
 +
\lnot p \lor \lnot q
 +
\end{matrix}</math>
 +
|-
 +
|
 +
<math>\begin{matrix}
 +
f_8
 +
\\[4pt]
 +
f_9
 +
\\[4pt]
 +
f_{10}
 +
\\[4pt]
 +
f_{11}
 +
\\[4pt]
 +
f_{12}
 +
\\[4pt]
 +
f_{13}
 +
\\[4pt]
 +
f_{14}
 +
\\[4pt]
 +
f_{15}
 +
\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
f_{1000}
 +
\\[4pt]
 +
f_{1001}
 +
\\[4pt]
 +
f_{1010}
 +
\\[4pt]
 +
f_{1011}
 +
\\[4pt]
 +
f_{1100}
 +
\\[4pt]
 +
f_{1101}
 +
\\[4pt]
 +
f_{1110}
 +
\\[4pt]
 +
f_{1111}
 +
\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
1~0~0~0
 +
\\[4pt]
 +
1~0~0~1
 +
\\[4pt]
 +
1~0~1~0
 +
\\[4pt]
 +
1~0~1~1
 +
\\[4pt]
 +
1~1~0~0
 +
\\[4pt]
 +
1~1~0~1
 +
\\[4pt]
 +
1~1~1~0
 +
\\[4pt]
 +
1~1~1~1
 +
\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
~~p~~q~~
 +
\\[4pt]
 +
((p,~q))
 +
\\[4pt]
 +
~~~~~q~~
 +
\\[4pt]
 +
~(p~(q))
 +
\\[4pt]
 +
~~p~~~~~
 +
\\[4pt]
 +
((p)~q)~
 +
\\[4pt]
 +
((p)(q))
 +
\\[4pt]
 +
((~))
 +
\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
p ~\text{and}~ q
 +
\\[4pt]
 +
p ~\text{equal to}~ q
 +
\\[4pt]
 +
q
 +
\\[4pt]
 +
\text{not}~ p ~\text{without}~ q
 +
\\[4pt]
 +
p
 +
\\[4pt]
 +
\text{not}~ q ~\text{without}~ p
 +
\\[4pt]
 +
p ~\text{or}~ q
 +
\\[4pt]
 +
\text{true}
 +
\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
p \land q
 +
\\[4pt]
 +
p = q
 +
\\[4pt]
 +
q
 +
\\[4pt]
 +
p \Rightarrow q
 +
\\[4pt]
 +
p
 +
\\[4pt]
 +
p \Leftarrow q
 +
\\[4pt]
 +
p \lor q
 +
\\[4pt]
 +
1
 +
\end{matrix}</math>
 
|}
 
|}
  

Revision as of 01:24, 23 August 2009

Logical Graphs

Truth Tables


\(\text{Table A1.}~~\text{Propositional Forms on Two Variables}\)

\(\mathcal{L}_1\)

\(\text{Decimal}\)

\(\mathcal{L}_2\)

\(\text{Binary}\)

\(\mathcal{L}_3\)

\(\text{Vector}\)

\(\mathcal{L}_4\)

\(\text{Cactus}\)

\(\mathcal{L}_5\)

\(\text{English}\)

\(\mathcal{L}_6\)

\(\text{Ordinary}\)

  \(p\colon\!\) \(1~1~0~0\!\)      
  \(q\colon\!\) \(1~0~1~0\!\)      

\(\begin{matrix} f_0 \\[4pt] f_1 \\[4pt] f_2 \\[4pt] f_3 \\[4pt] f_4 \\[4pt] f_5 \\[4pt] f_6 \\[4pt] f_7 \end{matrix}\)

\(\begin{matrix} f_{0000} \\[4pt] f_{0001} \\[4pt] f_{0010} \\[4pt] f_{0011} \\[4pt] f_{0100} \\[4pt] f_{0101} \\[4pt] f_{0110} \\[4pt] f_{0111} \end{matrix}\)

\(\begin{matrix} 0~0~0~0 \\[4pt] 0~0~0~1 \\[4pt] 0~0~1~0 \\[4pt] 0~0~1~1 \\[4pt] 0~1~0~0 \\[4pt] 0~1~0~1 \\[4pt] 0~1~1~0 \\[4pt] 0~1~1~1 \end{matrix}\)

\(\begin{matrix} (~) \\[4pt] (p)(q) \\[4pt] (p)~q~ \\[4pt] (p)~~~ \\[4pt] ~p~(q) \\[4pt] ~~~(q) \\[4pt] (p,~q) \\[4pt] (p~~q) \end{matrix}\)

\(\begin{matrix} \text{false} \\[4pt] \text{neither}~ p ~\text{nor}~ q \\[4pt] q ~\text{without}~ p \\[4pt] \text{not}~ p \\[4pt] p ~\text{without}~ q \\[4pt] \text{not}~ q \\[4pt] p ~\text{not equal to}~ q \\[4pt] \text{not both}~ p ~\text{and}~ q \end{matrix}\)

\(\begin{matrix} 0 \\[4pt] \lnot p \land \lnot q \\[4pt] \lnot p \land q \\[4pt] \lnot p \\[4pt] p \land \lnot q \\[4pt] \lnot q \\[4pt] p \ne q \\[4pt] \lnot p \lor \lnot q \end{matrix}\)

\(\begin{matrix} f_8 \\[4pt] f_9 \\[4pt] f_{10} \\[4pt] f_{11} \\[4pt] f_{12} \\[4pt] f_{13} \\[4pt] f_{14} \\[4pt] f_{15} \end{matrix}\)

\(\begin{matrix} f_{1000} \\[4pt] f_{1001} \\[4pt] f_{1010} \\[4pt] f_{1011} \\[4pt] f_{1100} \\[4pt] f_{1101} \\[4pt] f_{1110} \\[4pt] f_{1111} \end{matrix}\)

\(\begin{matrix} 1~0~0~0 \\[4pt] 1~0~0~1 \\[4pt] 1~0~1~0 \\[4pt] 1~0~1~1 \\[4pt] 1~1~0~0 \\[4pt] 1~1~0~1 \\[4pt] 1~1~1~0 \\[4pt] 1~1~1~1 \end{matrix}\)

\(\begin{matrix} ~~p~~q~~ \\[4pt] ((p,~q)) \\[4pt] ~~~~~q~~ \\[4pt] ~(p~(q)) \\[4pt] ~~p~~~~~ \\[4pt] ((p)~q)~ \\[4pt] ((p)(q)) \\[4pt] ((~)) \end{matrix}\)

\(\begin{matrix} p ~\text{and}~ q \\[4pt] p ~\text{equal to}~ q \\[4pt] q \\[4pt] \text{not}~ p ~\text{without}~ q \\[4pt] p \\[4pt] \text{not}~ q ~\text{without}~ p \\[4pt] p ~\text{or}~ q \\[4pt] \text{true} \end{matrix}\)

\(\begin{matrix} p \land q \\[4pt] p = q \\[4pt] q \\[4pt] p \Rightarrow q \\[4pt] p \\[4pt] p \Leftarrow q \\[4pt] p \lor q \\[4pt] 1 \end{matrix}\)


\(\text{Table 1.}~~\text{Logical Boundaries and Their Complements}\)
\(\mathcal{L}_1\) \(\mathcal{L}_2\) \(\mathcal{L}_3\) \(\mathcal{L}_4\)
Decimal Binary Sequential Parenthetical
  \(p =\!\) 1 1 1 1 0 0 0 0  
  \(q =\!\) 1 1 0 0 1 1 0 0  
  \(r =\!\) 1 0 1 0 1 0 1 0  
\(f_{104}\!\) \(f_{01101000}\!\) 0 1 1 0 1 0 0 0 \(( p , q , r )\!\)
\(f_{148}\!\) \(f_{10010100}\!\) 1 0 0 1 0 1 0 0 \(( p , q , (r))\!\)
\(f_{146}\!\) \(f_{10010010}\!\) 1 0 0 1 0 0 1 0 \(( p , (q), r )\!\)
\(f_{97}\!\) \(f_{01100001}\!\) 0 1 1 0 0 0 0 1 \(( p , (q), (r))\!\)
\(f_{134}\!\) \(f_{10000110}\!\) 1 0 0 0 0 1 1 0 \(((p), q , r )\!\)
\(f_{73}\!\) \(f_{01001001}\!\) 0 1 0 0 1 0 0 1 \(((p), q , (r))\!\)
\(f_{41}\!\) \(f_{00101001}\!\) 0 0 1 0 1 0 0 1 \(((p), (q), r )\!\)
\(f_{22}\!\) \(f_{00010110}\!\) 0 0 0 1 0 1 1 0 \(((p), (q), (r))\!\)
\(f_{233}\!\) \(f_{11101001}\!\) 1 1 1 0 1 0 0 1 \((((p), (q), (r)))\!\)
\(f_{214}\!\) \(f_{11010110}\!\) 1 1 0 1 0 1 1 0 \((((p), (q), r ))\!\)
\(f_{182}\!\) \(f_{10110110}\!\) 1 0 1 1 0 1 1 0 \((((p), q , (r)))\!\)
\(f_{121}\!\) \(f_{01111001}\!\) 0 1 1 1 1 0 0 1 \((((p), q , r ))\!\)
\(f_{158}\!\) \(f_{10011110}\!\) 1 0 0 1 1 1 1 0 \((( p , (q), (r)))\!\)
\(f_{109}\!\) \(f_{01101101}\!\) 0 1 1 0 1 1 0 1 \((( p , (q), r ))\!\)
\(f_{107}\!\) \(f_{01101011}\!\) 0 1 1 0 1 0 1 1 \((( p , q , (r)))\!\)
\(f_{151}\!\) \(f_{10010111}\!\) 1 0 0 1 0 1 1 1 \((( p , q , r ))\!\)


Work Area


\(\text{Table 1.}~~\text{Logical Boundaries and Their Complements}\)
\(\mathcal{L}_1\) \(\mathcal{L}_2\) \(\mathcal{L}_3\) \(\mathcal{L}_4\)
Decimal Binary Sequential Parenthetical
  \(p =\!\) 1 1 1 1 0 0 0 0  
  \(q =\!\) 1 1 0 0 1 1 0 0  
  \(r =\!\) 1 0 1 0 1 0 1 0  
\(f_{104}\!\) \(f_{01101000}\!\) 0 1 1 0 1 0 0 0 \(( p , q , r )\!\)
\(f_{148}\!\) \(f_{10010100}\!\) 1 0 0 1 0 1 0 0 \(( p , q , (r))\!\)
\(f_{146}\!\) \(f_{10010010}\!\) 1 0 0 1 0 0 1 0 \(( p , (q), r )\!\)
\(f_{97}\!\) \(f_{01100001}\!\) 0 1 1 0 0 0 0 1 \(( p , (q), (r))\!\)
\(f_{134}\!\) \(f_{10000110}\!\) 1 0 0 0 0 1 1 0 \(((p), q , r )\!\)
\(f_{73}\!\) \(f_{01001001}\!\) 0 1 0 0 1 0 0 1 \(((p), q , (r))\!\)
\(f_{41}\!\) \(f_{00101001}\!\) 0 0 1 0 1 0 0 1 \(((p), (q), r )\!\)
\(f_{22}\!\) \(f_{00010110}\!\) 0 0 0 1 0 1 1 0 \(((p), (q), (r))\!\)
\(f_{233}\!\) \(f_{11101001}\!\) 1 1 1 0 1 0 0 1 \((((p), (q), (r)))\!\)
\(f_{214}\!\) \(f_{11010110}\!\) 1 1 0 1 0 1 1 0 \((((p), (q), r ))\!\)
\(f_{182}\!\) \(f_{10110110}\!\) 1 0 1 1 0 1 1 0 \((((p), q , (r)))\!\)
\(f_{121}\!\) \(f_{01111001}\!\) 0 1 1 1 1 0 0 1 \((((p), q , r ))\!\)
\(f_{158}\!\) \(f_{10011110}\!\) 1 0 0 1 1 1 1 0 \((( p , (q), (r)))\!\)
\(f_{109}\!\) \(f_{01101101}\!\) 0 1 1 0 1 1 0 1 \((( p , (q), r ))\!\)
\(f_{107}\!\) \(f_{01101011}\!\) 0 1 1 0 1 0 1 1 \((( p , q , (r)))\!\)
\(f_{151}\!\) \(f_{10010111}\!\) 1 0 0 1 0 1 1 1 \((( p , q , r ))\!\)


\(\text{Table A1.}~~\text{Propositional Forms on Two Variables}\)

\(\mathcal{L}_1\)

\(\text{Decimal}\)

\(\mathcal{L}_2\)

\(\text{Binary}\)

\(\mathcal{L}_3\)

\(\text{Vector}\)

\(\mathcal{L}_4\)

\(\text{Cactus}\)

\(\mathcal{L}_5\)

\(\text{English}\)

\(\mathcal{L}_6\)

\(\text{Ordinary}\)

  \(p\colon\!\) \(1~1~0~0\!\)      
  \(q\colon\!\) \(1~0~1~0\!\)      

\(\begin{matrix} f_0 \\[4pt] f_1 \\[4pt] f_2 \\[4pt] f_3 \\[4pt] f_4 \\[4pt] f_5 \\[4pt] f_6 \\[4pt] f_7 \end{matrix}\)

\(\begin{matrix} f_{0000} \\[4pt] f_{0001} \\[4pt] f_{0010} \\[4pt] f_{0011} \\[4pt] f_{0100} \\[4pt] f_{0101} \\[4pt] f_{0110} \\[4pt] f_{0111} \end{matrix}\)

\(\begin{matrix} 0~0~0~0 \\[4pt] 0~0~0~1 \\[4pt] 0~0~1~0 \\[4pt] 0~0~1~1 \\[4pt] 0~1~0~0 \\[4pt] 0~1~0~1 \\[4pt] 0~1~1~0 \\[4pt] 0~1~1~1 \end{matrix}\)

\(\begin{matrix} (~) \\[4pt] (p)(q) \\[4pt] (p)~q~ \\[4pt] (p)~~~ \\[4pt] ~p~(q) \\[4pt] ~~~(q) \\[4pt] (p,~q) \\[4pt] (p~~q) \end{matrix}\)

\(\begin{matrix} \text{false} \\[4pt] \text{neither}~ p ~\text{nor}~ q \\[4pt] q ~\text{without}~ p \\[4pt] \text{not}~ p \\[4pt] p ~\text{without}~ q \\[4pt] \text{not}~ q \\[4pt] p ~\text{not equal to}~ q \\[4pt] \text{not both}~ p ~\text{and}~ q \end{matrix}\)

\(\begin{matrix} 0 \\[4pt] \lnot p \land \lnot q \\[4pt] \lnot p \land q \\[4pt] \lnot p \\[4pt] p \land \lnot q \\[4pt] \lnot q \\[4pt] p \ne q \\[4pt] \lnot p \lor \lnot q \end{matrix}\)

\(\begin{matrix} f_8 \\[4pt] f_9 \\[4pt] f_{10} \\[4pt] f_{11} \\[4pt] f_{12} \\[4pt] f_{13} \\[4pt] f_{14} \\[4pt] f_{15} \end{matrix}\)

\(\begin{matrix} f_{1000} \\[4pt] f_{1001} \\[4pt] f_{1010} \\[4pt] f_{1011} \\[4pt] f_{1100} \\[4pt] f_{1101} \\[4pt] f_{1110} \\[4pt] f_{1111} \end{matrix}\)

\(\begin{matrix} 1~0~0~0 \\[4pt] 1~0~0~1 \\[4pt] 1~0~1~0 \\[4pt] 1~0~1~1 \\[4pt] 1~1~0~0 \\[4pt] 1~1~0~1 \\[4pt] 1~1~1~0 \\[4pt] 1~1~1~1 \end{matrix}\)

\(\begin{matrix} ~~p~~q~~ \\[4pt] ((p,~q)) \\[4pt] ~~~~~q~~ \\[4pt] ~(p~(q)) \\[4pt] ~~p~~~~~ \\[4pt] ((p)~q)~ \\[4pt] ((p)(q)) \\[4pt] ((~)) \end{matrix}\)

\(\begin{matrix} p ~\text{and}~ q \\[4pt] p ~\text{equal to}~ q \\[4pt] q \\[4pt] \text{not}~ p ~\text{without}~ q \\[4pt] p \\[4pt] \text{not}~ q ~\text{without}~ p \\[4pt] p ~\text{or}~ q \\[4pt] \text{true} \end{matrix}\)

\(\begin{matrix} p \land q \\[4pt] p = q \\[4pt] q \\[4pt] p \Rightarrow q \\[4pt] p \\[4pt] p \Leftarrow q \\[4pt] p \lor q \\[4pt] 1 \end{matrix}\)


Venn Diagrams

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