Difference between revisions of "Logical equality"
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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 equality''' is an | + | '''Logical equality''' 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 operands are false or both operands are true. |
| − | The [[truth table]] of | + | The [[truth table]] of <math>p ~\operatorname{EQ}~ q,</math> also written as <math>p = q,\!</math> <math>p \Leftrightarrow q,\!</math> or <math>p \equiv 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 Equality}\!</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 = 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 || T | + | | <math>\operatorname{T}</math> || <math>\operatorname{T}</math> || <math>\operatorname{T}</math> |
|} | |} | ||
Revision as of 10:52, 15 May 2012
☞ This page belongs to resource collections on Logic and Inquiry.
Logical equality is an operation on two logical values, typically the values of two propositions, that produces a value of true if and only if both operands are false or both operands are true.
The truth table of \(p ~\operatorname{EQ}~ q,\) also written as \(p = q,\!\) \(p \Leftrightarrow q,\!\) or \(p \equiv q,\!\) is as follows:
| \(p\!\) | \(q\!\) | \(p = q\!\) |
| \(\operatorname{F}\) | \(\operatorname{F}\) | \(\operatorname{T}\) |
| \(\operatorname{F}\) | \(\operatorname{T}\) | \(\operatorname{F}\) |
| \(\operatorname{T}\) | \(\operatorname{F}\) | \(\operatorname{F}\) |
| \(\operatorname{T}\) | \(\operatorname{T}\) | \(\operatorname{T}\) |
Syllabus
Focal nodes
Template:Col-breakTemplate:Col-breakTemplate:Col-endPeer nodes
Logical 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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