User:Jon Awbrey/Figures and Tables 13

Venn Diagrams and Logical Graphs on Two Variables

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${\text{Venn Diagrams and Logical Graphs on Two Variables}}$

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${\text{Boolean Functions on Two Variables}}$

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

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${\text{Venn Diagrams and Logical Graphs on Two Variables}}~{\stackrel {_{\bullet }}{}}~{\text{Orbit Order}}$