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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