In boolean logic, logical nor or joint denial is a truthfunctional 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. In grammar, nor is a coordinating conjunction.
NOR  

Definition  
Truth table  
Logic gate  
Normal forms  
Disjunctive  
Conjunctive  
Zhegalkin polynomial  
Post's lattices  
0preserving  no 
1preserving  no 
Monotone  no 
Affine  no 
The NOR operator is also known as Peirce's arrow. Peirce, in unpublished manuscripts, first considered it as a logical operator, and showed that it can express logical NOT, AND, and OR. Stamm,^{[1]} Sheffer,^{[2]} and Nicod^{[3]} were the first to discuss it in print. Quine introduced the symbol for it.^{[4]} As with its dual, the NAND operator (a.k.a. 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). Other terms for the NOR operator include Quine's dagger, the ampheck (from Ancient Greek ἀμφήκης, amphēkēs, "cutting both ways") used by Peirce,^{[5]} and neithernor. Other ways of notating include, P NOR Q, and "Xpq" (in Bocheński notation).
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.^{[6]}
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.
The truth table of (also written as P NOR Q) is as follows:
True  True  False 
True  False  False 
False  True  False 
False  False  True 
The logical NOR is the negation of the disjunction:
Logical NOR does not possess any of the five qualities (truthpreserving, falsepreserving, linear, monotonic, selfdual) 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.
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:

 

