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.

signifies logical negation,

Non-disjunction is usually denoted as

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

), 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] 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.

is the negation of the disjunction: Peirce is the first to show the functional completeness of non-disjunction while he doesn't publish his result.

for non-disjunction (in fact, what Peirce himself used is

while Peirce's editors made such disambiguated use).

the ampheck (from Ancient Greek ἀμφήκης, amphēkēs, "cutting both ways").

[4] In 1911, Stamm [pl] 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.

[5][6] Note that most uses in logical notation of

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

So some people call it Webb operator,[7] Webb operation[8] or Webb function.

[10] So some people call the operator Peirce arrow or Quine dagger.

for non-disjunction in Polish notation.

[12] NOR is commutative but not associative, which means that

[13] The logical NOR, taken by itself, is a functionally complete set of connectives.

[14] This can be proved by first showing, with a truth table, that

,[15] the logical NOR suffices to define the set of connectives

,[15] which is shown to be truth-functionally complete by the Disjunctive Normal Form Theorem.

[15] This may also be seen from the fact that 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.

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.

, the usual operators of propositional logic are: