Logical NAND

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The logical NAND is an operation on two logical values, typically the values of two propositions, that produces a value of false if and only if both of its operands are true. In other words, it produces a value of true if and only if at least one of its operands is false.

The truth table of $p ~\operatorname{NAND}~ q,$ also written $p \stackrel{\circ}{\curlywedge} q\!$ or $p \barwedge q,\!$ appears below:

$\text{Logical NAND}\!$
$p\!$	$q\!$	$p \stackrel{\circ}{\curlywedge} q\!$
$\operatorname{F}$	$\operatorname{F}$	$\operatorname{T}$
$\operatorname{F}$	$\operatorname{T}$	$\operatorname{T}$
$\operatorname{T}$	$\operatorname{F}$	$\operatorname{T}$
$\operatorname{T}$	$\operatorname{T}$	$\operatorname{F}$

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