Non-Disjunction (NOR) ○◂ Entries

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Non-Disjunction (NOR) ○◂｜Definition｜1st｜20251119205401-00-⌔

Logical NOR - Wikipedia

Logical NOR

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In Boolean logic, logical NOR, ¹ non-disjunction, or joint denial¹ 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 $\neg (p\vee q)$ and $\neg p\wedge \neg q$, where the symbol $\neg$ signifies logical negation, $\vee$ signifies OR, and $\wedge$ signifies AND.

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

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

Printed 2026-06-28.

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Footnotes

1. Howson, Colin (1997). Logic with trees: an introduction to symbolic logic. London; New York: Routledge. p. 43. ISBN 978-0-415-13342-5. ↩ ↩²

2. Hall, Eldon C. (1996). Journey to the Moon: The History of the Apollo Guidance Computer. Reston, Virginia, USA: American Institute of Aeronautics and Astronautics. p. 196. ISBN 1-56347-185-X. ↩

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