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Animated Logical Graphs

Boolean Functions on Two Variables • Index Order

PNG

$\text{Boolean Functions on Two Variables}$

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$\text{Boolean Functions on Two Variables}$
$\text{Boolean Function}$ $\text{Entitative Graph}$ $\text{Existential Graph}$
$f_{0}$
$\text{false}$ $\text{false}$ $\text{false}$
$f_{1}$
$\text{neither}~ x ~\text{nor}~ y$ $\lnot (x \lor y)$ $\lnot x \land \lnot y$
$f_{2}$
$y ~\text{and not}~ x$ $\lnot x \land y$ $\lnot x \land y$
$f_{3}$
$\text{not}~ x$ $\lnot x$ $\lnot x$
$f_{4}$
$x ~\text{and not}~ y$ $x \land \lnot y$ $x \land \lnot y$
$f_{5}$
$\text{not}~ y$ $\lnot y$ $\lnot y$
$f_{6}$
$x ~\text{not equal to}~ y$ $x \ne y$ $x \ne y$
$f_{7}$
$\text{not both}~ x ~\text{and}~ y$ $\lnot x \lor \lnot y$ $\lnot (x \land y)$
$f_{8}$
$x ~\text{and}~ y$ $x \land y$ $x \land y$
$f_{9}$
$x ~\text{equal to}~ y$ $x = y$ $x = y$
$f_{10}$
$y$ $y$ $y$
$f_{11}$
$\text{if}~ x ~\text{then}~ y$ $x \Rightarrow y$ $x \Rightarrow y$
$f_{12}$
$x$ $x$ $x$
$f_{13}$
$\text{if}~ y ~\text{then}~ x$ $x \Leftarrow y$ $x \Leftarrow y$
$f_{14}$
$x ~\text{or}~ y$ $x \lor y$ $x \lor y$
$f_{15}$
$\text{true}$ $\text{true}$ $\text{true}$

Logical Graphs : Entitative and Existential Interpretations

PNG

$\text{Logical Graphs : Entitative and Existential Interpretations}$

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$\text{Logical Graphs : Entitative and Existential Interpretations}$
$\text{Logical Graph}$ $\text{Entitative Interpretation}$ $\text{Existential Interpretation}$
$\text{true}$ $\text{false}$
$\texttt{(} ~ \texttt{)}$ $f_{15}$ $f_{0}$
$\lnot x \lor \lnot y$ $\lnot x \land \lnot y$
$\texttt{(} x \texttt{)(} y \texttt{)}$ $f_{7}$ $f_{1}$
$x \Rightarrow y$ $x \nLeftarrow y$
$\texttt{(} x \texttt{)} y$ $f_{11}$ $f_{2}$
$\lnot x$ $\lnot x$
$\texttt{(} x \texttt{)}$ $f_{3}$ $f_{3}$
$x \Leftarrow y$ $x \nRightarrow y$
$x \texttt{(} y \texttt{)}$ $f_{13}$ $f_{4}$
$\lnot y$ $\lnot y$
$\texttt{(} y \texttt{)}$ $f_{5}$ $f_{5}$
$x = y$ $x \ne y$
$\texttt{(} x \texttt{,} y \texttt{)}$ $f_{9}$ $f_{6}$
$\lnot (x \lor y)$ $\lnot (x \land y)$
$\texttt{(} x y \texttt{)}$ $f_{1}$ $f_{7}$
$x \lor y$ $x \land y$
$x y$ $f_{14}$ $f_{8}$
$x \ne y$ $x = y$
$\texttt{((} x \texttt{,} y \texttt{))}$ $f_{6}$ $f_{9}$
$y$ $y$
$y$ $f_{10}$ $f_{10}$
$x \nLeftarrow y$ $x \Rightarrow y$
$\texttt{(} x \texttt{(} y \texttt{))}$ $f_{2}$ $f_{11}$
$x$ $x$
$x$ $f_{12}$ $f_{12}$
$x \nRightarrow y$ $x \Leftarrow y$
$\texttt{((} x \texttt{)} y \texttt{)}$ $f_{4}$ $f_{13}$
$x \land y$ $x \lor y$
$\texttt{((} x \texttt{)(} y \texttt{))}$ $f_{8}$ $f_{14}$
$\text{false}$ $\text{true}$
$f_{0}$ $f_{15}$

Boolean Functions on Two Variables • Orbit Order

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$\text{Boolean Functions on Two Variables : Orbit Order}$
$\text{Boolean Function}$ $\text{Entitative Graph}$ $\text{Existential Graph}$
$f_{0}$
$\text{false}$ $\text{false}$ $\text{false}$
$f_{1}$
$\text{neither}~ x ~\text{nor}~ y$ $\lnot (x \lor y)$ $\lnot x \land \lnot y$
$f_{2}$
$y ~\text{and not}~ x$ $\lnot x \land y$ $\lnot x \land y$
$f_{4}$
$x ~\text{and not}~ y$ $x \land \lnot y$ $x \land \lnot y$
$f_{8}$
$x ~\text{and}~ y$ $x \land y$ $x \land y$
$f_{3}$
$\text{not}~ x$ $\lnot x$ $\lnot x$
$f_{12}$
$x$ $x$ $x$
$f_{6}$
$x ~\text{not equal to}~ y$ $x \ne y$ $x \ne y$
$f_{9}$
$x ~\text{equal to}~ y$ $x = y$ $x = y$
$f_{5}$
$\text{not}~ y$ $\lnot y$ $\lnot y$
$f_{10}$
$y$ $y$ $y$
$f_{7}$
$\text{not both}~ x ~\text{and}~ y$ $\lnot x \lor \lnot y$ $\lnot (x \land y)$
$f_{11}$
$\text{if}~ x ~\text{then}~ y$ $x \Rightarrow y$ $x \Rightarrow y$
$f_{13}$
$\text{if}~ y ~\text{then}~ x$ $x \Leftarrow y$ $x \Leftarrow y$
$f_{14}$
$x ~\text{or}~ y$ $x \lor y$ $x \lor y$
$f_{15}$
$\text{true}$ $\text{true}$ $\text{true}$