# Work α

## Boolean Functions on Two Variables

### Index Order

#### PNG

$\text{Boolean Functions on Two Variables}$

#### HTML + JPG + LaTeX

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

### Orbit Order

#### PNG

$\text{Boolean Functions on Two Variables} \stackrel{_\bullet}{} \text{Orbit Order}$

#### HTML + JPG + LaTeX

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