NOR, also called Peirce's arrow (Zach 2016), is a connective in logic equivalent to the composition NOT OR that yields false if any condition
is true, and true if all conditions
are false. 
NOR 
is equivalent to 
,
where 
denotes NOT
and 
denotes OR.
In propositional calculus, the term joint denial is used to refer to the NOR connective.
Notations for NOR include 
and 
(Mendelson 1997, p. 26). The
NOR operation is implemented as Nor[A,
B, ...]. The circuit diagram symbol for a NOR gate is illustrated above.
The NOR binary operator has the following truth table (Simpson 1987, p. 547; Mendelson 1997, p. 26).
 |  |  |
| T | T | F |
| T | F | F |
| F | T | F |
| F | F | T |
The dual operation to NOR is NAND, also called the Sheffer stroke. Complementing both inputs and the output of NAND gives NOR,
 |
(1)
|
Like NAND, NOR is functionally complete. The operations NOT, OR, and AND can be expressed using only NOR,
 |  |  |
(2)
|
 |  |  |
(3)
|
 |  |  |
(4)
|
Consequently, every Boolean function of one or more variables can be expressed using only NOR.
