Editing Conjunction introduction

{{Infobox mathematical statement
| name = Conjunction introduction
| type = [[Rule of inference]]
| field = [[Propositional calculus]]
| statement = If the proposition <math>P</math> is true, and the proposition <math>Q</math> is true, then the logical conjunction of the two propositions <math>P</math> and <math>Q</math> is true.
| symbolic statement = <math>\frac{P,Q}{\therefore P \land Q}</math>
}}
{{Transformation rules}}

'''Conjunction introduction''' (often abbreviated simply as '''conjunction''' and also called '''and introduction''' or '''adjunction''')<ref>{{cite book |title=A Concise Introduction to Logic 4th edition |last=Hurley |first=Patrick |year=1991 |publisher=Wadsworth Publishing |pages=346–51 }}</ref><ref>{{cite book |last1=Copi |first1=Irving M. |last2=Cohen |first2=Carl |last3=McMahon |first3=Kenneth |title=Introduction to Logic|date=2014 |publisher=Pearson |isbn=978-1-292-02482-0 |edition=14th|pages=370, 620}}</ref><ref>{{cite book |last1=Moore |first1=Brooke Noel |last2=Parker |first2=Richard |title=Critical Thinking |date=2015 |publisher=McGraw Hill |location=New York |isbn=978-0-07-811914-9 |page=311 |edition=11th |chapter-url=https://archive.org/details/criticalthinking0000moor_t5e3/page/311/mode/1up |chapter-url-access=registration|chapter=Deductive Arguments II Truth-Functional Logic}}</ref> is a [[Validity (logic)|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]] <math>P</math> is true, and the proposition <math>Q</math> is true, then the logical conjunction of the two propositions <math>P</math> and <math>Q</math> is true. For example, if it is true that "it is raining", and it is true that "the cat is inside", then it is true that "it is raining and the cat is inside". The rule can be stated:

:<math>\frac{P,Q}{\therefore P \land Q}</math>

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 \land Q</math>" can be placed on a subsequent line.

== Formal notation ==
The ''conjunction introduction'' rule may be written in [[sequent]] notation:

: <math>P, Q \vdash P \land Q</math>

where <math>P</math> and <math>Q</math> are propositions expressed in some [[formal system]], and <math>\vdash</math> is a [[metalogic]]al [[Symbol (formal)|symbol]] meaning that <math>P \land 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]];

==References==
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{{logic-stub}}
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[[Category:Rules of inference]]
[[Category:Theorems in propositional logic]]