Editing Logical NOR (section)

{{Short description|Binary operation that is true if and only if both operands are false}}
{{About|NOR in the logical sense|the electronic gate|NOR gate|other uses|Nor (disambiguation){{!}}Nor}}
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{{Infobox logical connective
| title        = Logical NOR
| other titles = NOR
| wikifunction = Z10231
| Venn diagram = Venn1000.svg
| definition   = <math>\overline{x + y}</math>
| truth table  = <math>(0001)</math>
| logic gate   = NOR_ANSI.svg
| DNF          = <math>\overline{x} \cdot \overline{y}</math>
| CNF          = <math>\overline{x} \cdot \overline{y}</math>
| Zhegalkin    = <math>1 \oplus x \oplus y \oplus xy</math>
| 0-preserving = no
| 1-preserving = no
| monotone     = no
| affine       = no
| self-dual    = no
}}
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{{C. S. Peirce articles}}
In [[Boolean logic]], '''logical NOR''','''<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>''' '''non-disjunction''', or '''joint denial<ref name=":13" />''' is a truth-functional operator which produces a result that is the negation of [[logical disjunction|logical or]]. That is, a sentence of the form (''p'' NOR ''q'') is true precisely when neither ''p'' nor ''q'' is true—i.e. when both ''p'' and ''q'' are ''false''. It is logically equivalent to <math>\neg(p \lor q)</math> and <math>\neg p \land \neg q</math>, where the symbol <math>\neg</math> signifies logical [[negation]], <math>\lor</math> signifies [[logical disjunction|OR]], and <math>\land</math> signifies [[logical conjunction|AND]].

Non-disjunction is usually denoted as <math>\downarrow</math> or <math>\overline{\vee}</math> or <math>X</math> (prefix) or <math>\operatorname{NOR}</math>.

As with its [[duality (mathematics)|dual]], the [[NAND operator]] (also known as the [[Sheffer stroke]]—symbolized as either <math>\uparrow</math>, <math>\mid</math> or <math>/</math>), NOR can be used by itself, without any other logical operator, to constitute a logical [[formal system]] (making NOR [[functional completeness|functionally complete]]).

The [[computer]] used in the spacecraft that first carried humans to the [[moon]], the [[Apollo Guidance Computer]], was constructed entirely using NOR gates with three inputs.<ref name="Hall_1996"/>