Logical NOR
In Boolean logic, logical NOR or 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 of p and q are false. It is logically equivalent to  and , where the symbol  signifies logical negation,  signifies OR, and  signifies AND.

Non-disjunction is usually denoted as  or  or  (prefix) or .

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

Definition
The NOR operation is a logical operation on two logical values, typically the values of two propositions, that produces a value of true if and only if both operands are false. In other words, it produces a value of false if and only if at least one operand is true.

Truth table
The truth table of  is as follows:

Logical equivalences
The logical NOR  is the negation of the disjunction:

Alternative notations and names
Peirce is the first to show the functional completeness of non-disjunction while he doesn't publish his result. Peirce used  for non-conjunction and  for non-disjunction (in fact, what Peirce himself used is  and he didn't introduce  while Peirce's editors made such disambiguated use). Peirce called   as  (from Ancient Greek , , "cutting both ways").

In 1911,  was the first to publish a description of both non-conjunction (using , the Stamm hook), and non-disjunction (using , the Stamm star), and showed their functional completeness.</ref> Note that most uses in logical notation of  use this for negation.

In 1913, Sheffer described non-disjunction and showed its functional completeness. Sheffer used  for non-conjunction, and  for non-disjunction.

In 1935, Webb described non-disjunction for -valued logic, and use  for the operator. So some people call it Webb operator, Webb operation or Webb function.

In 1940, Quine also described non-disjunction and use  for the operator. So some people call the operator Peirce arrow or Quine dagger.

In 1944, Church also described non-disjunction and use  for the operator.

In 1954, Bocheński  used  in  for non-disjunction in  Polish notation.

Properties
Logical NOR does not possess any of the five qualities (truth-preserving, false-preserving, linear, monotonic, self-dual) required to be absent from at least one member of a set of functionally complete operators. Thus, the set containing only NOR suffices as a complete set.

Other Boolean operations in terms of the logical NOR
NOR has the interesting feature that all other logical operators can be expressed by interlaced NOR operations. The logical NAND operator also has this ability.

Expressed in terms of NOR , the usual operators of propositional logic are:

See also
 Bitwise NOR
 Boolean algebra
 Boolean domain
 Boolean function
 Functional completeness
 NOR gate
 Propositional logic
 Sole sufficient operator
 Sheffer stroke as symbol for the logical NAND

References

External links
 

NOR
Charles Sanders Peirce

de:Peirce-Funktion
it:Algebra di Boole#NOR