Implies

Implies is a logical binary operation which takes two values of the set of $\mathbb{Z}/2$ and applies the “implies” function which only returns 0 if True implies False.

The operation is noted as $\Rightarrow$ throughout my work. \Rightarrow in LaTeX.

Arg 1	Arg 2	Return
$1$	$1$	$1$
$1$	$0$	$0$
$0$	$1$	$1$
$0$	$0$	$1$
Truth table of Implies

Decomposition of Implies

It is well know that $x\Rightarrow y=\neg x\vee y$. This can easily be verified as they share the same truth table.