Logical NOR

In <a href="/facts/Boolean_logic/VkCToAmg">Boolean logic</a>, logical NOR, non-disjunction, or joint denial is a truth-functional operator which produces a result that is the negation of <a href="/facts/Logical_disjunction/jbI2EGlM">logical or</a>. 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 
 
 
 
 ¬
 (
 p
 ∨
 q
 )
 
 
 {\displaystyle \neg (p\lor q)}
 
 and 
 
 
 
 ¬
 p
 ∧
 ¬
 q
 
 
 {\displaystyle \neg p\land \neg q}
 
, where the symbol 
 
 
 
 ¬
 
 
 {\displaystyle \neg }
 
 signifies logical <a href="/facts/Negation/q5AQBvBj">negation</a>, 
 
 
 
 ∨
 
 
 {\displaystyle \lor }
 
 signifies <a href="/facts/Logical_disjunction/jbI2EGlM">OR</a>, and 
 
 
 
 ∧
 
 
 {\displaystyle \land }
 
 signifies <a href="/facts/Logical_conjunction/62uyyn1d">AND</a>.
Non-disjunction is usually denoted as 
 
 
 
 ↓
 
 
 {\displaystyle \downarrow }
 
 or 
 
 
 
 
 
 ∨
 ¯
 
 
 
 
 {\displaystyle {\overline {\vee }}}
 
 or 
 
 
 
 X
 
 
 {\displaystyle X}
 
 (prefix) or 
 
 
 
 NOR
 
 
 {\displaystyle \operatorname {NOR} }
 
.
As with its <a href="/facts/Duality_(mathematics)/8jGuyQIU">dual</a>, the <a href="/facts/NAND_operator/rpXH07u4">NAND operator</a> (also known as the <a href="/facts/Sheffer_stroke/rpXH07u4">Sheffer stroke</a>—symbolized as either 
 
 
 
 ↑
 
 
 {\displaystyle \uparrow }
 
, 
 
 
 
 ∣
 
 
 {\displaystyle \mid }
 
 or 
 
 
 
 
 /
 
 
 
 {\displaystyle /}
 
), NOR can be used by itself, without any other logical operator, to constitute a logical <a href="/facts/Formal_system/KaeDAjK7">formal system</a> (making NOR <a href="/facts/Functional_completeness/ncyHAsHH">functionally complete</a>).
The <a href="/facts/Computer/SQe1aK05">computer</a> used in the spacecraft that first carried humans to the <a href="/facts/Moon/zKHqEMPb">moon</a>, the <a href="/facts/Apollo_Guidance_Computer/xGxHlrXY">Apollo Guidance Computer</a>, was constructed entirely using NOR gates with three inputs.

Logical NOR open-in-new

Logical NOR