Editing Sheffer stroke (section)

{{short description|Logical operation}}
{{use dmy dates|date=May 2023|cs1-dates=y}}
{{use list-defined references|date=May 2023}}
{{Infobox logical connective
| title        = Sheffer stroke
| other titles = NAND
| wikifunction = Z10243
| Venn diagram = Venn1110.svg
| definition   = <math>\overline{x \cdot y}</math>
| truth table  = <math>(0111)</math>
| logic gate   = NAND_ANSI.svg
| DNF          = <math>\overline{x} + \overline{y}</math>
| CNF          = <math>\overline{x} + \overline{y}</math>
| Zhegalkin    = <math>1 \oplus xy</math>
| 0-preserving = no
| 1-preserving = no
| monotone     = no
| affine       = no
| self-dual    = no
}}
{{Logical connectives sidebar}}

In [[Boolean function]]s and [[propositional calculus]], the '''Sheffer stroke''' denotes a [[logical operation]] that is equivalent to the [[logical negation|negation]] of the [[logical conjunction|conjunction]] operation, expressed in ordinary language as "not both". It is also called '''non-conjunction''', '''alternative denial''' (since it says in effect that at least one of its operands is false), or '''NAND''' ("not and").<ref name=":13">{{Cite book |last=Howson |first=Colin |title=Logic with trees: an introduction to symbolic logic |date=1997 |publisher=Routledge |isbn=978-0-415-13342-5 |location=London; New York |pages=43}}</ref> In [[digital electronics]], it corresponds to the [[NAND gate]]. It is named after [[Henry Maurice Sheffer]] and written as <math>\mid</math> or as <math>\uparrow</math> or as <math>\overline{\wedge}</math> or as <math>Dpq</math> in [[Polish notation]] by [[Jan Łukasiewicz|Łukasiewicz]] (but not as ||, often used to represent [[logical disjunction|disjunction]]).

Its [[duality (mathematics)|dual]] is the [[logical NOR|NOR operator]] (also known as the [[Peirce arrow]], [[Quine dagger]] or [[Webb operator]]). Like its dual, 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.