Sheffer stroke

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In Boolean functions and propositional calculus, the Sheffer stroke, named after Henry M. Sheffer, written "|" (see vertical bar) 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 operation ("not and").

Like its dual, the NOR operator (a.k.a. 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 NAND flash memory and computer processor design.


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Definition

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.

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