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

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==Truth Tables==
 
==Truth Tables==
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<br>
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{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:90%"
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|+ <math>\text{Table A1.}~~\text{Propositional Forms on Two Variables}</math>
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|- style="background:#f0f0ff"
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| width="15%" |
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<p><math>\mathcal{L}_1</math></p>
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<p><math>\text{Decimal}</math></p>
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| width="15%" |
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<p><math>\mathcal{L}_2</math></p>
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<p><math>\text{Binary}</math></p>
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| width="15%" |
 +
<p><math>\mathcal{L}_3</math></p>
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<p><math>\text{Vector}</math></p>
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| width="15%" |
 +
<p><math>\mathcal{L}_4</math></p>
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<p><math>\text{Cactus}</math></p>
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| width="25%" |
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<p><math>\mathcal{L}_5</math></p>
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<p><math>\text{English}</math></p>
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| width="15%" |
 +
<p><math>\mathcal{L}_6</math></p>
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<p><math>\text{Ordinary}</math></p>
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|- style="background:#f0f0ff"
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| &nbsp;
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| align="right" | <math>p\colon\!</math>
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| <math>1~1~0~0\!</math>
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| &nbsp;
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| &nbsp;
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| &nbsp;
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|- style="background:#f0f0ff"
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| &nbsp;
 +
| align="right" | <math>q\colon\!</math>
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| <math>1~0~1~0\!</math>
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| &nbsp;
 +
| &nbsp;
 +
| &nbsp;
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|-
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|
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<math>\begin{matrix}
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f_0
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\\[4pt]
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f_1
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\\[4pt]
 +
f_2
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\\[4pt]
 +
f_3
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\\[4pt]
 +
f_4
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\\[4pt]
 +
f_5
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\\[4pt]
 +
f_6
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\\[4pt]
 +
f_7
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\end{matrix}</math>
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|
 +
<math>\begin{matrix}
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f_{0000}
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\\[4pt]
 +
f_{0001}
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\\[4pt]
 +
f_{0010}
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\\[4pt]
 +
f_{0011}
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\\[4pt]
 +
f_{0100}
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\\[4pt]
 +
f_{0101}
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\\[4pt]
 +
f_{0110}
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\\[4pt]
 +
f_{0111}
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\end{matrix}</math>
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|
 +
<math>\begin{matrix}
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0~0~0~0
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\\[4pt]
 +
0~0~0~1
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\\[4pt]
 +
0~0~1~0
 +
\\[4pt]
 +
0~0~1~1
 +
\\[4pt]
 +
0~1~0~0
 +
\\[4pt]
 +
0~1~0~1
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\\[4pt]
 +
0~1~1~0
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\\[4pt]
 +
0~1~1~1
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\end{matrix}</math>
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|
 +
<math>\begin{matrix}
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(~)
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\\[4pt]
 +
(p)(q)
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\\[4pt]
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(p)~q~
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\\[4pt]
 +
(p)~~~
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\\[4pt]
 +
~p~(q)
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\\[4pt]
 +
~~~(q)
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\\[4pt]
 +
(p,~q)
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\\[4pt]
 +
(p~~q)
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\end{matrix}</math>
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|
 +
<math>\begin{matrix}
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\text{false}
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\\[4pt]
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\text{neither}~ p ~\text{nor}~ q
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\\[4pt]
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q ~\text{without}~ p
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\\[4pt]
 +
\text{not}~ p
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\\[4pt]
 +
p ~\text{without}~ q
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\\[4pt]
 +
\text{not}~ q
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\\[4pt]
 +
p ~\text{not equal to}~ q
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\\[4pt]
 +
\text{not both}~ p ~\text{and}~ q
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\end{matrix}</math>
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|
 +
<math>\begin{matrix}
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0
 +
\\[4pt]
 +
\lnot p \land \lnot q
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\\[4pt]
 +
\lnot p \land q
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\\[4pt]
 +
\lnot p
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\\[4pt]
 +
p \land \lnot q
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\\[4pt]
 +
\lnot q
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\\[4pt]
 +
p \ne q
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\\[4pt]
 +
\lnot p \lor \lnot q
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\end{matrix}</math>
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|-
 +
|
 +
<math>\begin{matrix}
 +
f_8
 +
\\[4pt]
 +
f_9
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\\[4pt]
 +
f_{10}
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\\[4pt]
 +
f_{11}
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\\[4pt]
 +
f_{12}
 +
\\[4pt]
 +
f_{13}
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\\[4pt]
 +
f_{14}
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\\[4pt]
 +
f_{15}
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\end{matrix}</math>
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|
 +
<math>\begin{matrix}
 +
f_{1000}
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\\[4pt]
 +
f_{1001}
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\\[4pt]
 +
f_{1010}
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\\[4pt]
 +
f_{1011}
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\\[4pt]
 +
f_{1100}
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\\[4pt]
 +
f_{1101}
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\\[4pt]
 +
f_{1110}
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\\[4pt]
 +
f_{1111}
 +
\end{matrix}</math>
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|
 +
<math>\begin{matrix}
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1~0~0~0
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\\[4pt]
 +
1~0~0~1
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\\[4pt]
 +
1~0~1~0
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\\[4pt]
 +
1~0~1~1
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\\[4pt]
 +
1~1~0~0
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\\[4pt]
 +
1~1~0~1
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\\[4pt]
 +
1~1~1~0
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\\[4pt]
 +
1~1~1~1
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\end{matrix}</math>
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|
 +
<math>\begin{matrix}
 +
~~p~~q~~
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\\[4pt]
 +
((p,~q))
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\\[4pt]
 +
~~~~~q~~
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\\[4pt]
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~(p~(q))
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\\[4pt]
 +
~~p~~~~~
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\\[4pt]
 +
((p)~q)~
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\\[4pt]
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((p)(q))
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\\[4pt]
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((~))
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\end{matrix}</math>
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|
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<math>\begin{matrix}
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p ~\text{and}~ q
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\\[4pt]
 +
p ~\text{equal to}~ q
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\\[4pt]
 +
q
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\\[4pt]
 +
\text{not}~ p ~\text{without}~ q
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\\[4pt]
 +
p
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\\[4pt]
 +
\text{not}~ q ~\text{without}~ p
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\\[4pt]
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p ~\text{or}~ q
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\\[4pt]
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\text{true}
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\end{matrix}</math>
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|
 +
<math>\begin{matrix}
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p \land q
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\\[4pt]
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p = q
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\\[4pt]
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q
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\\[4pt]
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p \Rightarrow q
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\\[4pt]
 +
p
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\\[4pt]
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p \Leftarrow q
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\\[4pt]
 +
p \lor q
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\\[4pt]
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1
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\end{matrix}</math>
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|}
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<br>
  
 
==Venn Diagrams==
 
==Venn Diagrams==

Revision as of 01:10, 23 August 2009

Logical Graphs

Truth Tables


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

\(\mathcal{L}_1\)

\(\text{Decimal}\)

\(\mathcal{L}_2\)

\(\text{Binary}\)

\(\mathcal{L}_3\)

\(\text{Vector}\)

\(\mathcal{L}_4\)

\(\text{Cactus}\)

\(\mathcal{L}_5\)

\(\text{English}\)

\(\mathcal{L}_6\)

\(\text{Ordinary}\)

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

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

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

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

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

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

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

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

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

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

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

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

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


Venn Diagrams

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