Difference between revisions of "Logical disjunction"
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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 disjunction''', also called '''logical alternation''', is an | + | '''Logical disjunction''', also called '''logical alternation''', 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 false. |
| − | The [[truth table]] of | + | The [[truth table]] of <math>p ~\operatorname{OR}~ q</math> (also written as <math>p \lor 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 Disjunction}\!</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 \lor q</math> | |
|- | |- | ||
| − | | F || F || F | + | | <math>\operatorname{F}</math> || <math>\operatorname{F}</math> || <math>\operatorname{F}</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 || T | + | | <math>\operatorname{T}</math> || <math>\operatorname{T}</math> || <math>\operatorname{T}</math> |
|} | |} | ||
Revision as of 01:52, 15 May 2012
☞ This page belongs to resource collections on Logic and Inquiry.
Logical disjunction, also called logical alternation, 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 false.
The truth table of \(p ~\operatorname{OR}~ q\) (also written as \(p \lor q\!\)) is as follows:
| \(p\!\) | \(q\!\) | \(p \lor q\) |
| \(\operatorname{F}\) | \(\operatorname{F}\) | \(\operatorname{F}\) |
| \(\operatorname{F}\) | \(\operatorname{T}\) | \(\operatorname{T}\) |
| \(\operatorname{T}\) | \(\operatorname{F}\) | \(\operatorname{T}\) |
| \(\operatorname{T}\) | \(\operatorname{T}\) | \(\operatorname{T}\) |
Syllabus
Focal nodes
Template:Col-breakTemplate:Col-breakTemplate:Col-endPeer nodes
- Logical Disjunction @ MyWikiBiz
- Logical Disjunction @ MathWeb Wiki
- Logical Disjunction @ NetKnowledge
- Logical Disjunction @ OER Commons
- Logical Disjunction @ P2P Foundation
- Logical Disjunction @ 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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