Difference between revisions of "Logical conjunction"
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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]]. | ||
| − | '''Logical conjunction''' is an | + | '''Logical conjunction''' is an operation on two logical values, typically the values of two [[proposition]]s, that produces a value of ''true'' if and only if both of its operands are true. |
| − | The [[truth table]] of | + | The [[truth table]] of <math>p ~\operatorname{AND}~ q</math> (also written as <math>p \land q\!</math> or <math>p \cdot q\!</math>) is as follows: |
<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 Conjunction}\!</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 \land q</math> | |
|- | |- | ||
| − | | F || F || F | + | | <math>\operatorname{F}</math> || <math>\operatorname{F}</math> || <math>\operatorname{F}</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 || T | + | | <math>\operatorname{T}</math> || <math>\operatorname{T}</math> || <math>\operatorname{T}</math> |
|} | |} | ||
Revision as of 16:58, 14 May 2012
☞ This page belongs to resource collections on Logic and Inquiry.
Logical conjunction 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 true.
The truth table of \(p ~\operatorname{AND}~ q\) (also written as \(p \land q\!\) or \(p \cdot q\!\)) is as follows:
| \(p\!\) | \(q\!\) | \(p \land q\) |
| \(\operatorname{F}\) | \(\operatorname{F}\) | \(\operatorname{F}\) |
| \(\operatorname{F}\) | \(\operatorname{T}\) | \(\operatorname{F}\) |
| \(\operatorname{T}\) | \(\operatorname{F}\) | \(\operatorname{F}\) |
| \(\operatorname{T}\) | \(\operatorname{T}\) | \(\operatorname{T}\) |
Syllabus
Focal nodes
Template:Col-breakTemplate:Col-breakTemplate:Col-endPeer nodes
- Logical Conjunction @ MyWikiBiz
- Logical Conjunction @ MathWeb Wiki
- Logical Conjunction @ NetKnowledge
- Logical Conjunction @ OER Commons
- Logical Conjunction @ P2P Foundation
- Logical Conjunction @ SemanticWeb
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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