Logical NOR information

Logical NOR
NOR
Definition
Truth table
Logic gate
Normal forms
Disjunctive
Conjunctive
Zhegalkin polynomial
Post's lattices
0-preserving	no
1-preserving	no
Monotone	no
Affine	no
	v; t; e;

In Boolean logic, logical NOR,^[1] non-disjunction, or joint denial^[1] is a truth-functional operator which produces a result that is the negation of 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 $\neg (p\lor q)$ and $\neg p\land \neg q$ , where the symbol $\neg$ signifies logical negation, $\lor$ signifies OR, and $\land$ signifies AND.

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

As with its dual, the NAND operator (also known as the Sheffer stroke—symbolized as either $\uparrow$ , $\mid$ or $/$ ), NOR can be used by itself, without any other logical operator, to constitute a logical formal system (making NOR 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.^[2]

^ ^a ^b Howson, Colin (1997). Logic with trees: an introduction to symbolic logic. London ; New York: Routledge. p. 43. ISBN 978-0-415-13342-5.
^ Cite error: The named reference Hall_1996 was invoked but never defined (see the help page).

[:13-1] Howson, Colin (1997). Logic with trees: an introduction to symbolic logic. London ; New York: Routledge. p. 43. ISBN 978-0-415-13342-5.

[Hall_1996-2] Cite error: The named reference Hall_1996 was invoked but never defined (see the help page).

Logical NOR information

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Definition	${\overline {x+y}}$
Truth table	$(0001)$
Logic gate
Normal forms
Disjunctive	${\overline {x}}\cdot {\overline {y}}$
Conjunctive	${\overline {x}}\cdot {\overline {y}}$
Zhegalkin polynomial	$1\oplus x\oplus y\oplus xy$
Post's lattices
0-preserving	no
1-preserving	no
Monotone	no
Affine	no
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Charles Sanders Peirce
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