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'''Conjunction introduction''' (often abbreviated simply as '''conjunction'''<ref>{{cite book |title=A Concise Introduction to Logic 4th edition |last=Hurley |first=Patrick |authorlink= |coauthors= |year=1991 |publisher=Wadsworth Publishing |location= |isbn= |page= |pages=346–51 |url= |accessdate=}}</ref><ref>Copi and Cohen</ref><ref>Moore and Parker</ref>) is a [[validity|valid]] [[rule of inference]] of [[propositional calculus|propositional logic]]. The rule makes it possible to introduce a [[logical conjunction|conjunction]] into a [[Formal proof|logical proof]]. It is the [[inference]] that if the [[proposition]] ''p'' is true, and proposition ''q'' is true, then the logical conjunction of the two propositions ''p and q'' is true. For example, if it's true that it's raining, and it's true that I'm inside, then it's true that "it's raining and I'm inside". The rule can be stated:
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:<math>\frac{P,Q}{\therefore P \and Q}</math>
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where the rule is that wherever an instance of "<math>P</math>" and "<math>Q</math>" appear on lines of a proof, a "<math>P \and Q</math>" can be placed on a subsequent line.
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== Formal notation ==
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The ''conjunction introduction'' rule may be written in [[sequent]] notation:
 
 
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: <math>P, Q \vdash P \and Q</math>
 
 
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where <math>\vdash</math> is a [[metalogic]]al [[Symbol (formal)|symbol]] meaning that <math>P \and Q</math> is a [[logical consequence|syntactic consequence]] if <math>P</math> and <math>Q</math> are each on lines of a proof in some [[formal system|logical system]];
 
 
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where <math>P</math> and <math>Q</math> are propositions expressed in some logical system.
 
 
</ul>
==References==
{{reflist}}
 
{{DEFAULTSORT:Conjunction Introduction}}
[[Category:Rules of inference]]

Latest revision as of 19:04, 13 December 2014

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