# Logical NAND

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

 ${\displaystyle p\!}$ ${\displaystyle q\!}$ ${\displaystyle p{\stackrel {\circ }{\curlywedge }}q\!}$ ${\displaystyle \operatorname {F} }$ ${\displaystyle \operatorname {F} }$ ${\displaystyle \operatorname {T} }$ ${\displaystyle \operatorname {F} }$ ${\displaystyle \operatorname {T} }$ ${\displaystyle \operatorname {T} }$ ${\displaystyle \operatorname {T} }$ ${\displaystyle \operatorname {F} }$ ${\displaystyle \operatorname {T} }$ ${\displaystyle \operatorname {T} }$ ${\displaystyle \operatorname {T} }$ ${\displaystyle \operatorname {F} }$

## Document history

Portions of the above article were adapted from the following sources under the GNU Free Documentation License, under other applicable licenses, or by permission of the copyright holders.