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→Logical NNOR
==Logical NNOR==
==Logical NNOR==
The ''[[logical NNOR]]'' is a [[logical operation]] on two [[logical value]]s, typically the values of two [[proposition]]s, that produces a value of ''true'' if and only if both of its operands are false. In other words, it produces a value of ''false'' if and only if at least one of its operands is true.
The '''[[logical NNOR]]''' (“Neither Nor”) is an operation on two logical values, typically the values of two propositions, that produces a value of ''true'' if and only if both of its operands are false. In other words, it produces a value of ''false'' if and only if at least one of its operands is true.
The truth table of '''p NNOR q''' (also written as '''p ⊥ q''' or '''p ↓ q''') is as follows:
The truth table of <math>p ~\operatorname{NNOR}~ q,</math> also written <math>p \curlywedge q,\!</math> appears below:
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{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; font-weight:bold; text-align:center; width:45%"
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:45%"
|+ '''Logical NNOR'''
|+ style="height:30px" | <math>\text{Logical NNOR}\!</math>
|- style="background:#e6e6ff"
|- style="height:40px; background:#f0f0ff"
| style="width:33%" | <math>p\!</math>
| style="width:33%" | <math>q\!</math>
| style="width:33%" | <math>p \curlywedge q\!</math>
|-
|-
| F || F || T
| <math>\operatorname{F}</math> || <math>\operatorname{F}</math> || <math>\operatorname{T}</math>
|-
|-
| F || T || F
| <math>\operatorname{F}</math> || <math>\operatorname{T}</math> || <math>\operatorname{F}</math>
|-
|-
| T || F || F
| <math>\operatorname{T}</math> || <math>\operatorname{F}</math> || <math>\operatorname{F}</math>
|-
|-
| T || T || F
| <math>\operatorname{T}</math> || <math>\operatorname{T}</math> || <math>\operatorname{F}</math>
|}
|}