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Animated Logical Graphs

Boolean Functions on Two Variables • Index Order

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$\text{Boolean Functions on Two Variables}$

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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

PNG

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