Difference between revisions of "Logical conjunction"

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<font size="3">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].
 
<font size="3">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].
  
'''Logical conjunction''' is an [[logical operation|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 true.
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'''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 '''p AND q''' (also written as '''p &and; q''', '''p & q''', or '''p<math>\cdot</math>q''') is as follows:
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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:
  
 
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<br>
  
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; font-weight:bold; text-align:center; width:45%"
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{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:45%"
|+ '''Logical Conjunction'''
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|+ style="height:30px" | <math>\text{Logical Conjunction}\!</math>
|- style="background:#e6e6ff"
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|- style="height:40px; background:#f0f0ff"
! style="width:15%" | p
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| style="width:33%" | <math>p\!</math>
! style="width:15%" | q
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| style="width:33%" | <math>q\!</math>
! style="width:15%" | p &and; q
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| style="width:33%" | <math>p \land q</math>
 
|-
 
|-
| F || F || F
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| <math>\operatorname{F}</math> || <math>\operatorname{F}</math> || <math>\operatorname{F}</math>
 
|-
 
|-
| F || T || F
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| <math>\operatorname{F}</math> || <math>\operatorname{T}</math> || <math>\operatorname{F}</math>
 
|-
 
|-
| T || F || F
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| <math>\operatorname{T}</math> || <math>\operatorname{F}</math> || <math>\operatorname{F}</math>
 
|-
 
|-
| T || T || T
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| <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:


\(\text{Logical Conjunction}\!\)
\(p\!\) \(q\!\) \(p \land q\)
\(\operatorname{F}\) \(\operatorname{F}\) \(\operatorname{F}\)
\(\operatorname{F}\) \(\operatorname{T}\) \(\operatorname{F}\)
\(\operatorname{T}\) \(\operatorname{F}\) \(\operatorname{F}\)
\(\operatorname{T}\) \(\operatorname{T}\) \(\operatorname{T}\)


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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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