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en>Monkbot: /* Definition */Task 5: Fix CS1 deprecated coauthor parameter errors

2014-07-24T09:10:02Z

Definition: Task 5: Fix CS1 deprecated coauthor parameter errors

← Older revision		Revision as of 11:10, 24 July 2014
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	~~std home test Hello and welcome~~. My title is ~~Numbers~~ [http://~~theoffshoremanual~~.com/~~?testimonial=know-facing-candida-albicans~~ at home std ~~test~~] ~~Wunder. She is a librarian but~~ [http://~~nxnn~~.~~info~~/~~blog~~/~~284637 nxnn~~.~~info~~] ~~she~~'s usually ~~needed~~ her home std test personal company. ~~One of~~ the ~~very very best things in the globe for him is to gather badges but he~~ is ~~struggling to find time for it. Minnesota has usually been his home but his wife wants them to move.<br><br>Visit my web page - over the~~ [http://www.~~Aafp~~.org/~~afp~~/~~2000~~/~~0315~~/~~p1708~~.~~html counter~~ std] test ([http://~~www~~.~~egitimpark~~.~~net/siir~~/~~groups~~/~~clear~~-up-a-~~candida~~-~~with~~-~~these-tips/ click through the following article~~])		Greetings. The writer's title is Phebe and she feels comfy [http://premium.asslikethat.com/user/CSalerno at home std testing] when people use [http://www.pponline.co.uk/user/miriamlinswkucrd www.pponline.co.uk] the complete title. Puerto Rico is where he's usually been residing but she needs to move because of her family members. She is a librarian home std test kit but she's always wanted her personal company. over the counter std test The factor she std home test adores most is [http://www.mtnstopshiv.org/sites/default/files/attachments/Herpes%20Brochure_Body_High%20Res.pdf physique developing] and now she is trying to make cash with it.<br><br>Here is my weblog - home std test [[http://support.kaponline.com/entries/46228144-Endocrine-Illnesses-Canines-Part-1 Read Webpage]]

en>Materialscientist: Reverted edits by 203.91.196.239 (talk) to last version by 35.2.77.241

2014-02-27T04:55:04Z

Reverted edits by 203.91.196.239 (talk) to last version by 35.2.77.241

← Older revision		Revision as of 06:55, 27 February 2014
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	~~In [[propositional calculus\|propositional logic]], the '''commutativity of conjunction''' is a [[validity\|valid]] [[argument form]]~~ and ~~truth-functional [[tautology (logic)\|tautology]]~~. It is ~~considered to be a law of~~ [~~[classical logic]]~~. It is the principle that the conjuncts of a [[logical conjunction]] may switch places with each other, while preserving the [[truth-value]] of the resulting proposition.<ref>{{cite book\|title=Introduction to Mathematical Logic\|author=Elliott Mendelson\|year=1997\|publisher=CRC Press\|isbn=0-~~412~~-~~80830~~-~~7}}</ref>~~		std home test Hello and welcome. My title is Numbers [http://theoffshoremanual.com/?testimonial=know-facing-candida-albicans at home std test] Wunder. She is a librarian but [http://nxnn.info/blog/284637 nxnn.info] she's usually needed her home std test personal company. One of the very very best things in the globe for him is to gather badges but he is struggling to find time for it. Minnesota has usually been his home but his wife wants them to move.<br><br>Visit my web page - over the [http://www.Aafp.org/afp/2000/0315/p1708.html counter std] test ([http://www.egitimpark.net/siir/groups/clear-up-a-candida-with-these-tips/ click through the following article])

	~~== Formal notation ==~~

	~~''Commutativity of conjunction'' can be expressed in [~~[~~sequent]] notation as~~:

	~~: <math>(P \and Q) \vdash (Q \and P)<~~/~~math>~~

	~~and~~

	~~: <math>(Q \and P) \vdash (P \and Q)<~~/~~math>~~

	~~where <math>\vdash<~~/~~math> is a [[metalogic]]al symbol meaning that <math>(Q \and P)<~~/~~math> is a [[logical consequence\|syntactic consequence]~~] of ~~<math>(P \and Q)</math>,~~ in the ~~one case, and <math>(P \and Q)</math>~~ is ~~a syntactic consequence of <math>(Q \and P)</math> in the other, in some [[formal system\|logical system]];~~

	~~or in [[rule of inference\|rule form]]:~~

	~~:<math>\frac{P \and Q}{\therefore Q \and P}</math>~~

	~~and~~

	~~:<math>\frac{Q \and P}{\therefore P \and Q}</math>~~

	~~where the rule~~ is ~~that wherever an instance of "<math>(P \and Q)</math>" appears on a line of a proof,~~ it ~~can be replaced with "~~<~~math~~>~~(Q \and P)~~<~~/math~~>~~" and wherever an instance of "<math>(Q \and P)</math>" appears on a line of a proof, it can be replaced with "<math>(P \and Q)</math>";~~

	~~or as~~ the ~~statement of a truth-functional tautology or [~~[~~theorem]] of propositional logic:~~

	:~~<math>(P \and Q) \to (Q \and P)<~~/~~math>~~

	~~and~~

	~~:<math>(Q \and P) \to (P \and Q)<~~/~~math>~~

	~~where <math>P<~~/~~math> and <math>Q<~~/~~math> are [[proposition]]s expressed in some formal system.~~

	~~== Generalized principle ==~~
	~~For any propositions H<sub>1<~~/~~sub>, H<sub>2<~~/~~sub>,~~ .~~.. H<sub>''n''</sub>, and permutation σ~~(~~n) of the numbers 1 through n, it is the case that~~:

	~~:H<sub>1<~~/~~sub> <math>\land</math> H<sub>2<~~/~~sub> <math>\land</math> .~~.. ~~<math>\land</math> H<sub>n</sub>~~

	~~is equivalent to~~

	~~:H<sub>σ(1)<~~/~~sub> <math>\land<~~/~~math> H<sub>σ(2)<~~/~~sub> <math>\land<~~/~~math> H<sub>σ(n)</sub>.~~

	~~For example, if H<sub>1</sub> is~~
	~~:''It is raining''~~

	~~H<sub>2</sub> is~~
	~~:''[[Socrates]] is mortal''~~

	~~and H<sub>3</sub> is~~
	~~:''2+2=4''~~

	~~then~~

	~~''It is raining and Socrates is mortal and 2+2=4''~~

	~~is equivalent to~~

	~~''Socrates is mortal and 2+2=4 and it is raining''~~

	~~and the other orderings of~~ the ~~predicates.~~

	~~==References==~~
	~~{{reflist}}~~

	~~[[Category:Classical logic]]~~
	~~[[Category:Rules of inference]]~~
	~~[[Category:Theorems in propositional logic]~~]

en>Kvng: Reverted good faith edits by 64.28.140.34 (talk): Not enough improvement to merit altering cited quote. (TW)

2013-04-11T15:29:16Z

Reverted good faith edits by 64.28.140.34 (talk): Not enough improvement to merit altering cited quote. (TW)

← Older revision		Revision as of 17:29, 11 April 2013
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	~~Hello~~ and ~~welcome~~. ~~My name~~ is ~~Irwin and I totally dig~~ that title~~. For years I~~'~~ve been operating~~ as a ~~payroll clerk. What I adore doing~~ is ~~playing baseball but I haven't produced~~ a ~~dime~~ with it~~. Her family members lives in Minnesota.~~<br><br>~~Also visit my webpage~~; ~~over~~ the ~~counter std test~~ ([~~http~~://~~Www~~.~~videokeren~~.~~com~~/~~blog~~/~~14593 More Tips~~])		In [[propositional calculus\|propositional logic]], the '''commutativity of conjunction''' is a [[validity\|valid]] [[argument form]] and truth-functional [[tautology (logic)\|tautology]]. It is considered to be a law of [[classical logic]]. It is the principle that the conjuncts of a [[logical conjunction]] may switch places with each other, while preserving the [[truth-value]] of the resulting proposition.<ref>{{cite book\|title=Introduction to Mathematical Logic\|author=Elliott Mendelson\|year=1997\|publisher=CRC Press\|isbn=0-412-80830-7}}</ref>

			== Formal notation ==

			''Commutativity of conjunction'' can be expressed in [[sequent]] notation as:

			: <math>(P \and Q) \vdash (Q \and P)</math>

			and

			: <math>(Q \and P) \vdash (P \and Q)</math>

			where <math>\vdash</math> is a [[metalogic]]al symbol meaning that <math>(Q \and P)</math> is a [[logical consequence\|syntactic consequence]] of <math>(P \and Q)</math>, in the one case, and <math>(P \and Q)</math> is a syntactic consequence of <math>(Q \and P)</math> in the other, in some [[formal system\|logical system]];

			or in [[rule of inference\|rule form]]:

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

			and

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

			where the rule is that wherever an instance of "<math>(P \and Q)</math>" appears on a line of a proof, it can be replaced with "<math>(Q \and P)</math>" and wherever an instance of "<math>(Q \and P)</math>" appears on a line of a proof, it can be replaced with "<math>(P \and Q)</math>";

			or as the statement of a truth-functional tautology or [[theorem]] of propositional logic:

			:<math>(P \and Q) \to (Q \and P)</math>

			and

			:<math>(Q \and P) \to (P \and Q)</math>

			where <math>P</math> and <math>Q</math> are [[proposition]]s expressed in some formal system.

			== Generalized principle ==
			For any propositions H<sub>1</sub>, H<sub>2</sub>, ... H<sub>''n''</sub>, and permutation σ(n) of the numbers 1 through n, it is the case that:

			:H<sub>1</sub> <math>\land</math> H<sub>2</sub> <math>\land</math> ... <math>\land</math> H<sub>n</sub>

			is equivalent to

			:H<sub>σ(1)</sub> <math>\land</math> H<sub>σ(2)</sub> <math>\land</math> H<sub>σ(n)</sub>.

			For example, if H<sub>1</sub> is
			:''It is raining''

			H<sub>2</sub> is
			:''[[Socrates]] is mortal''

			and H<sub>3</sub> is
			:''2+2=4''

			then

			''It is raining and Socrates is mortal and 2+2=4''

			is equivalent to

			''Socrates is mortal and 2+2=4 and it is raining''

			and the other orderings of the predicates.

			==References==
			{{reflist}}

			[[Category:Classical logic]]
			[[Category:Rules of inference]]
			[[Category:Theorems in propositional logic]]

en>Helpful Pixie Bot: ISBNs (Build KE)

2012-05-10T12:42:46Z

ISBNs (Build KE)

New page

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