Concept

Logical NOR

Overview

In Boolean logic, logical NOR, non-disjunction, or joint denial 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

(

∨

)

{\displaystyle \neg (p\lor q)}

and

∧

{\displaystyle \neg p\land \neg q}

, where the symbol

{\displaystyle \neg }

signifies logical negation,

∨

{\displaystyle \lor }

signifies OR, and

∧

{\displaystyle \land }

signifies AND.

Non-disjunction is usually denoted as

↓

{\displaystyle \downarrow }

∨

{\displaystyle {\overline {\vee }}}

{\displaystyle X}

(prefix) or

NOR

{\displaystyle \operatorname {NOR} }

As with its dual, the NAND operator (also known as the Sheffer stroke—symbolized as either

↑

{\displaystyle \uparrow }

∣

{\displaystyle \mid }

{\displaystyle /}

), 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.

Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).

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In the ordinary sense of the term, by thought we generally represent to ourselves something more than simple and unmixed thought; we mean some thought, the material of which is from experience. Whereas in logic a thought is understood to include nothing else but what depends on thinking and what thinking has brought into existence. It is in these circumstances that thoughts are _pure_ thoughts.
Georg Wilhelm Friedrich Hegel, The Logic of Hegel
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The chief business of the logician is to classify arguments; for all testing clearly depends on classification. The classes of the logicians are defined by certain typical forms called syllogisms. For example, the syllogism called _Barbara_ is as follows: S is M; M is P: Hence, S is P. Or, to put words for letters— Enoch and Elijah were men; all men die: Hence, Enoch and Elijah must have died.
Charles S. Peirce, Chance, Love, and Logic
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Obj. 2: Further, whatever is true, is true by reason of truth. If, then, truth is only in the intellect, nothing will be true except in so far as it is understood. But this is the error of the ancient philosophers, who said that whatever seems to be true is so. Consequently mutual contradictories seem to be true as seen by different persons at the same time. Obj.
Aquinas Thomas, Summa Theologica, Part I
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Logical NOR

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