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:
 * it is not the case that $p$ and $q$ are both true.

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

Also known as
The symbol $\uparrow$ is sometimes known as the Sheffer stroke, named after, 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 portrayed.

Note that the actual original Sheffer stroke is in fact the $\mid$ symbol.

Also see

 * Definition:Logical NOR


 * Definition:Contrary Statements