Difference between revisions of "Logical NAND"
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<font size="3">☞</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]]. | <font size="3">☞</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]]. | ||
| − | The '''logical NAND''' is | + | The '''logical NAND''' is an operation on two logical values, typically the values of two [[proposition]]s, that produces a value of ''false'' if and only if both of its operands are true. In other words, it produces a value of ''true'' if and only if at least one of its operands is false. |
| − | The [[truth table]] of | + | The [[truth table]] of <math>p ~\operatorname{NAND}~ q,</math> also written <math>p \stackrel{\circ}{\curlywedge} q\!</math> or <math>p \barwedge q\!</math> appears below: |
<br> | <br> | ||
| − | {| align="center" border="1" cellpadding="8" cellspacing="0" style=" | + | {| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:45%" |
| − | |+ | + | |+ style="height:30px" | <math>\text{Logical NAND}\!</math> |
| − | |- style="background:# | + | |- style="height:40px; background:#f0f0ff" |
| − | + | | style="width:33%" | <math>p\!</math> | |
| − | + | | style="width:33%" | <math>q\!</math> | |
| − | + | | style="width:33%" | <math>p \stackrel{\circ}{\curlywedge} q\!</math> | |
|- | |- | ||
| − | | F || F || T | + | | <math>\operatorname{F}</math> || <math>\operatorname{F}</math> || <math>\operatorname{T}</math> |
|- | |- | ||
| − | | F || T || T | + | | <math>\operatorname{F}</math> || <math>\operatorname{T}</math> || <math>\operatorname{T}</math> |
|- | |- | ||
| − | | T || F || T | + | | <math>\operatorname{T}</math> || <math>\operatorname{F}</math> || <math>\operatorname{T}</math> |
|- | |- | ||
| − | | T || T || F | + | | <math>\operatorname{T}</math> || <math>\operatorname{T}</math> || <math>\operatorname{F}</math> |
|} | |} | ||
Revision as of 14:26, 15 May 2012
☞ This page belongs to resource collections on Logic and Inquiry.
The logical NAND is an operation on two logical values, typically the values of two propositions, that produces a value of false if and only if both of its operands are true. In other words, it produces a value of true if and only if at least one of its operands is false.
The truth table of \(p ~\operatorname{NAND}~ q,\) also written \(p \stackrel{\circ}{\curlywedge} q\!\) or \(p \barwedge q\!\) appears below:
| \(p\!\) | \(q\!\) | \(p \stackrel{\circ}{\curlywedge} q\!\) |
| \(\operatorname{F}\) | \(\operatorname{F}\) | \(\operatorname{T}\) |
| \(\operatorname{F}\) | \(\operatorname{T}\) | \(\operatorname{T}\) |
| \(\operatorname{T}\) | \(\operatorname{F}\) | \(\operatorname{T}\) |
| \(\operatorname{T}\) | \(\operatorname{T}\) | \(\operatorname{F}\) |
Syllabus
Focal nodes
Template:Col-breakTemplate:Col-breakTemplate:Col-endPeer nodes
Logical operators
Related topics
- Propositional calculus
- Sole sufficient operator
- Truth table
- Universe of discourse
- Zeroth order logic
Relational concepts
Information, Inquiry
Related articles
Document history
Portions of the above article were adapted from the following sources under the GNU Free Documentation License, under other applicable licenses, or by permission of the copyright holders.
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