Conjunction introduction: Difference between revisions
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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: | |||
:<math>\frac{P,Q}{\therefore P \and 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 \and 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 \and Q</math> | |||
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]]; | |||
where <math>P</math> and <math>Q</math> are propositions expressed in some logical system. | |||
==References== | |||
{{reflist}} | |||
{{DEFAULTSORT:Conjunction Introduction}} | |||
[[Category:Rules of inference]] | |||
Revision as of 12:14, 6 July 2013
Conjunction introduction (often abbreviated simply as conjunction[1][2][3]) is a valid rule of inference of propositional logic. The rule makes it possible to introduce a conjunction into a 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:
where the rule is that wherever an instance of "" and "" appear on lines of a proof, a "" can be placed on a subsequent line.
Formal notation
The conjunction introduction rule may be written in sequent notation:
where is a metalogical symbol meaning that is a syntactic consequence if and are each on lines of a proof in some logical system;
where and are propositions expressed in some logical system.
References
43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ Copi and Cohen
- ↑ Moore and Parker