Biconditional

Bicondition, or bicon, or if and only if, or iff is a logical binary operation which takes two values of the set of $\mathbb{Z}/2$ and applies the biconditional function which only returns 1 if both operands are the same and will otherwise return 0.

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

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

Inversion of xor

Note that the truth values of $⟺$ are the exact same as $\otimes$ but negated.

Decomposition of Bicon

See Decomposition of Implies $x⟺y=(x\wedge y)\vee (\neg x\wedge \neg y)$