Sheffer stroke

In Boolean functions and propositional calculus, the Sheffer stroke, named after Henry M. Sheffer, written "|" (see vertical bar, not to be confused with "||" which is often used to represent disjunction), "Dpq", or "↑" (an upwards arrow), 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 nand ("not and") or 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 operation.

Like its dual, the NOR operator (also known as the Peirce arrow or Quine dagger), NAND can be used by itself, without any other logical operator, to constitute a logical formal system (making NAND functionally complete). This property makes the NAND gate crucial to modern digital electronics, including its use in computer processor design.

The NAND operation is a logical operation on two logical values. It produces a value of true, if — and only if — at least one of the propositions is false.

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