The Sheffer stroke, written "|" or "↑", denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as "not both". It is also called the alternative denial, since it says in effect that at least one of its operands is false. In boolean algebra and digital electronics it is known as the NAND ("not and") operation. It is one of several sole sufficient operators that can be used to express all of the boolean functions that are the subject matter of propositional logic. Along with NOR, it is one of the two functionally complete binary operators of propositional logic.

The stroke is named for Henry M. Sheffer, who proved (Sheffer 1913) that all the usual operators of propositional logic (not, and, or, implies, and so on), could be expressed in terms of it. Charles Peirce (1880) had discovered this fact more than 30 years earlier, but never published his finding. Peirce also observed that all boolean operators could be defined in terms of the NOR operator, the dual of NAND.

The NAND operation is a logical 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 NAND q (also written as p | q or p ↑ q) is as follows:





One way of expressing p NAND q is a $overline$, where the symbol $cdot$ signifies AND and the line over the expression signifies not, the logical negation of that expression.

NAND is not used in everyday sentences because it exhibits an inherent inversion, which makes it confusing like a double negative. Here's an example of a sentence using the NAND operator:

We will surely die if we have food nand water.