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| | ==Truth Tables== | | ==Truth Tables== |
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| − | ===Version 3?=== | + | ===New Version=== |
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| | <br> | | <br> |
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| | <math>\begin{matrix} | | <math>\begin{matrix} |
| − | \texttt{( p , q , r )} | + | \texttt{(~p~,~q~,~r~)} |
| | \\[4pt] | | \\[4pt] |
| − | \texttt{( p , q , (r))} | + | \texttt{(~p~,~q~,(r))} |
| | \\[4pt] | | \\[4pt] |
| − | \texttt{( p , (q), r )} | + | \texttt{(~p~,(q),~r~)} |
| | \\[4pt] | | \\[4pt] |
| − | \texttt{( p , (q), (r))} | + | \texttt{(~p~,(q),(r))} |
| | \\[4pt] | | \\[4pt] |
| − | \texttt{((p), q , r )} | + | \texttt{((p),~q~,~r~)} |
| | \\[4pt] | | \\[4pt] |
| − | \texttt{((p), q , (r))} | + | \texttt{((p),~q~,(r))} |
| | \\[4pt] | | \\[4pt] |
| − | \texttt{((p), (q), r )} | + | \texttt{((p),(q),~r~)} |
| | \\[4pt] | | \\[4pt] |
| − | \texttt{((p), (q), (r))} | + | \texttt{((p),(q),(r))} |
| | \end{matrix}</math> | | \end{matrix}</math> |
| | |- | | |- |
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| | <math>\begin{matrix} | | <math>\begin{matrix} |
| − | \texttt{(((p), (q), (r)))} | + | \texttt{(((p),(q),(r)))} |
| | \\[4pt] | | \\[4pt] |
| − | \texttt{(((p), (q), r ))} | + | \texttt{(((p),(q),~r~))} |
| | \\[4pt] | | \\[4pt] |
| − | \texttt{(((p), q , (r)))} | + | \texttt{(((p),~q~,(r)))} |
| | \\[4pt] | | \\[4pt] |
| − | \texttt{(((p), q , r ))} | + | \texttt{(((p),~q~,~r~))} |
| | \\[4pt] | | \\[4pt] |
| − | \texttt{(( p , (q), (r)))} | + | \texttt{((~p~,(q),(r)))} |
| | \\[4pt] | | \\[4pt] |
| − | \texttt{(( p , (q), r ))} | + | \texttt{((~p~,(q),~r~))} |
| | \\[4pt] | | \\[4pt] |
| − | \texttt{(( p , q , (r)))} | + | \texttt{((~p~,~q~,(r)))} |
| | \\[4pt] | | \\[4pt] |
| − | \texttt{(( p , q , r ))} | + | \texttt{((~p~,~q~,~r~))} |
| | \end{matrix}</math> | | \end{matrix}</math> |
| | |} | | |} |
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| | <br> | | <br> |
| | | | |
| − | ===Version 2=== | + | ===Old Version=== |
| − | | |
| − | <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 1.}~~\text{Logical Boundaries and Their Complements}</math>
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| − | |- style="background:#f0f0ff"
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| − | | <math>\mathcal{L}_1</math>
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| − | | <math>\mathcal{L}_2</math>
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| − | | <math>\mathcal{L}_3</math>
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| − | | <math>\mathcal{L}_4</math>
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| − | |- style="background:#f0f0ff"
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| − | |
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| − | | align="right" | <math>p\colon\!</math>
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| − | | <math>1~1~1~1~0~0~0~0</math>
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| − | |
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| − | |- style="background:#f0f0ff"
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| − | |
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| − | | align="right" | <math>q\colon\!</math>
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| − | | <math>1~1~0~0~1~1~0~0</math>
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| − | |
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| − | |- style="background:#f0f0ff"
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| − | |
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| − | | align="right" | <math>r\colon\!</math>
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| − | | <math>1~0~1~0~1~0~1~0</math>
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| − | |
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| − | |-
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| − | |
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| − | <math>\begin{matrix}
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| − | f_{104}
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| − | \\[4pt]
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| − | f_{148}
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| − | \\[4pt]
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| − | f_{146}
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| − | \\[4pt]
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| − | f_{97}
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| − | \\[4pt]
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| − | f_{134}
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| − | \\[4pt]
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| − | f_{73}
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| − | \\[4pt]
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| − | f_{41}
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| − | \\[4pt]
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| − | f_{22}
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| − | \end{matrix}</math>
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| − | |
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| − | <math>\begin{matrix}
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| − | f_{01101000}
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| − | \\[4pt]
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| − | f_{10010100}
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| − | \\[4pt]
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| − | f_{10010010}
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| − | \\[4pt]
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| − | f_{01100001}
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| − | \\[4pt]
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| − | f_{10000110}
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| − | \\[4pt]
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| − | f_{01001001}
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| − | \\[4pt]
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| − | f_{00101001}
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| − | \\[4pt]
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| − | f_{00010110}
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| − | \end{matrix}</math>
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| − | |
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| − | <math>\begin{matrix}
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| − | 0~1~1~0~1~0~0~0
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| − | \\[4pt]
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| − | 1~0~0~1~0~1~0~0
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| − | \\[4pt]
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| − | 1~0~0~1~0~0~1~0
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| − | \\[4pt]
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| − | 0~1~1~0~0~0~0~1
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| − | \\[4pt]
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| − | 1~0~0~0~0~1~1~0
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| − | \\[4pt]
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| − | 0~1~0~0~1~0~0~1
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| − | \\[4pt]
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| − | 0~0~1~0~1~0~0~1
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| − | \\[4pt]
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| − | 0~0~0~1~0~1~1~0
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| − | \end{matrix}</math>
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| − | |
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| − | <math>\begin{matrix}
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| − | ( p , q , r )
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| − | \\[4pt]
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| − | ( p , q , (r))
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| − | \\[4pt]
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| − | ( p , (q), r )
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| − | \\[4pt]
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| − | ( p , (q), (r))
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| − | \\[4pt]
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| − | ((p), q , r )
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| − | \\[4pt]
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| − | ((p), q , (r))
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| − | \\[4pt]
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| − | ((p), (q), r )
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| − | \\[4pt]
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| − | ((p), (q), (r))
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| − | \end{matrix}</math>
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| − | |-
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| − | |
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| − | <math>\begin{matrix}
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| − | f_{233}
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| − | \\[4pt]
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| − | f_{214}
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| − | \\[4pt]
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| − | f_{182}
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| − | \\[4pt]
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| − | f_{121}
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| − | \\[4pt]
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| − | f_{158}
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| − | \\[4pt]
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| − | f_{109}
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| − | \\[4pt]
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| − | f_{107}
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| − | \\[4pt]
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| − | f_{151}
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| − | \end{matrix}</math>
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| − | |
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| − | <math>\begin{matrix}
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| − | f_{11101001}
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| − | \\[4pt]
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| − | f_{11010110}
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| − | \\[4pt]
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| − | f_{10110110}
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| − | \\[4pt]
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| − | f_{01111001}
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| − | \\[4pt]
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| − | f_{10011110}
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| − | \\[4pt]
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| − | f_{01101101}
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| − | \\[4pt]
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| − | f_{01101011}
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| − | \\[4pt]
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| − | f_{10010111}
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| − | \end{matrix}</math>
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| − | |
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| − | <math>\begin{matrix}
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| − | 1~1~1~0~1~0~0~1
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| − | \\[4pt]
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| − | 1~1~0~1~0~1~1~0
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| − | \\[4pt]
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| − | 1~0~1~1~0~1~1~0
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| − | \\[4pt]
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| − | 0~1~1~1~1~0~0~1
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| − | \\[4pt]
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| − | 1~0~0~1~1~1~1~0
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| − | \\[4pt]
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| − | 0~1~1~0~1~1~0~1
| |
| − | \\[4pt]
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| − | 0~1~1~0~1~0~1~1
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| − | \\[4pt]
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| − | 1~0~0~1~0~1~1~1
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| − | \end{matrix}</math>
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| − | |
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| − | <math>\begin{matrix}
| |
| − | (((p), (q), (r)))
| |
| − | \\[4pt]
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| − | (((p), (q), r ))
| |
| − | \\[4pt]
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| − | (((p), q , (r)))
| |
| − | \\[4pt]
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| − | (((p), q , r ))
| |
| − | \\[4pt]
| |
| − | (( p , (q), (r)))
| |
| − | \\[4pt]
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| − | (( p , (q), r ))
| |
| − | \\[4pt]
| |
| − | (( p , q , (r)))
| |
| − | \\[4pt]
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| − | (( p , q , r ))
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| − | \end{matrix}</math>
| |
| − | |}
| |
| − | | |
| − | <br>
| |
| − | | |
| − | ===Version 1===
| |
| | | | |
| | <br> | | <br> |
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| | <p>[[Image:Venn Diagram (P,Q,R).jpg|500px]]</p> | | <p>[[Image:Venn Diagram (P,Q,R).jpg|500px]]</p> |
| − | <p><math>\text{Figure 2.} ~~ \texttt{(} p \texttt{,} q \texttt{,} r \texttt{)}</math> | + | <p><math>\text{Figure 2.}~~\texttt{(p, q, r)}</math> |
| | |} | | |} |
| | | | |
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| | <p>[[Image:Venn Diagram ((P),(Q),(R)).jpg|500px]]</p> | | <p>[[Image:Venn Diagram ((P),(Q),(R)).jpg|500px]]</p> |
| − | <p><math>\text{Figure 3.} ~~ \texttt{((} p \texttt{),(} q \texttt{),(} r \texttt{))}</math> | + | <p><math>\text{Figure 3.}~~\texttt{((p),(q),(r))}</math> |
| | |} | | |} |
| | | | |
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| | <p><math>\text{Figure 3.} ~~ \texttt{((} p \texttt{),(} q \texttt{),(} r \texttt{))}</math> | | <p><math>\text{Figure 3.} ~~ \texttt{((} p \texttt{),(} q \texttt{),(} r \texttt{))}</math> |
| | |} | | |} |
| | + | |
| | + | * |
