Definition:Logical NAND

Definition
NAND (that is, not and), is a binary connective, written symbolically as $p \uparrow q$, whose behaviour is as follows:


 * $p \uparrow q$

is defined as:
 * $p$ and $q$ are not both true.

$p \uparrow q$ is voiced:
 * $p$ nand $q$

Boolean Interpretation
From the above, we see that the boolean interpretations for $\mathbf A \uparrow \mathbf B$ under the model $\mathcal M$ are:


 * $\left({\mathbf A \uparrow \mathbf B}\right)_\mathcal M = \begin{cases}

F & : \mathbf A_\mathcal M = T \text{ and } \mathbf B_\mathcal M = T \\ T & : \text {otherwise} \end{cases}$

Complement
The complement of $\uparrow$ is the conjunction operator.

Truth Function
The NAND connective defines the truth function $f^\uparrow$ as follows:

Also known as
The symbol $\uparrow$ is known as the Sheffer stroke, named after Henry Sheffer, who proved the important result that NAND is Functionally Complete.

Some authors even refer to the NAND operation itself as the Sheffer stroke function, but it can be argued that this conflation of the notation with the operation it is intended to denote can cause confusion, and can obscure the idea that is being protrayed.