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:''For the [[theorem]] of [[propositional calculus|propositional logic]] which expresses Disjunction elimination, see [[Case analysis]]''.
 
In [[propositional logic]], '''disjunction elimination'''<ref>http://www.wordiq.com/definition/Disjunction_elimination</ref><ref>http://www.lawrence.edu/dept/philosophy/research/ryckmant/Disjunction%20Elimination.htm</ref><ref>http://www.cs.gsu.edu/~cscskp/Automata/proofs/node6.html</ref> (sometimes named '''proof by cases''' or '''case analysis'''), is the [[validity|valid]] [[argument form]] and [[rule of inference]] that allows one to eliminate a [[logical disjunction|disjunctive statement]] from a [[formal proof|logical proof]]. It is the [[inference]] that  if a statement <math>P</math> implies a statement <math>Q</math> and a statement <math>R</math> also implies <math>Q</math>, then if either <math>P</math> or <math>R</math> is true, then <math>Q</math> has to be true. The reasoning is simple: since at least one of the statements P and R is true, and since either of them would be sufficient to entail Q, Q is certainly true.
 
:If I'm inside, I have my wallet on me.
:If I'm outside, I have my wallet on me.
:It is true that either I'm inside or I'm outside.
:Therefore, I have my wallet on me.
 
It is the rule can be stated as:
 
:<math>\frac{P \to Q, R \to Q, P \or R}{\therefore Q}</math>
 
where the rule is that whenever instances of "<math>P \to Q</math>", and "<math>R \to Q</math>" and "<math>P \or R</math>" appear on lines of a proof, "<math>Q</math>" can be placed on a subsequent line.
 
== Formal notation ==
The ''disjunction elimination'' rule may be written in [[sequent]] notation:
 
: <math>(P \to Q), (R \to Q), (P \or R) \vdash Q</math>
 
where <math>\vdash</math> is a [[metalogic]]al symbol meaning that <math>Q</math> is a [[logical consequence|syntactic consequence]] of <math>P \to Q</math>, and <math>R \to Q</math> and <math>P \or R</math> in some logical system;
 
and expressed as a truth-functional [[tautology (logic)|tautology]] or theorem of propositional logic:
 
:<math>(((P \to Q) \and (R \to Q)) \and (P \or R)) \to Q</math>
 
where <math>P</math>, <math>Q</math>, and <math>R</math> are propositions expressed in some [[formal system]].
 
==See also==
* [[Disjunction]]
* [[Argument in the alternative]]
* [[Disjunct normal form]]
 
==References==
{{Reflist}}
 
{{DEFAULTSORT:Disjunction Elimination}}
[[Category:Rules of inference]]

Revision as of 15:06, 24 February 2014

We may agree with me when I say which the total calories burned doing sit-ups can be determined by the amount of time invested on it. However, time isn't the only element responsible for helping you burn calories. If you are consistent inside the workout and provide moderate to vigorous strength, we can actually make certain that that the exercise is functioning. But constantly doing sit-ups, which too at a vigorous pace would not be possible for many. Which is why, if you truly want to make this exercise function for you, the best thing we can do is join abs classes inside the gym or get a fitness DVD.

While several of you are looking for how to lose fat out there inside the market, others are absolutely utilizing it by walking about calorie burn calculator their neighborhood plus burning calories everyday. Taking a walk each morning is advised for burning calories plus we can get healthy with the fresh air about we.

Maintaining a advantageous posture is the key to walking right. Stand erect with a chin parallel to the ground. This manner of strolling, with all the head held significant and straight is crucial for preserving a superior balance for the body. Keep a shoulders relaxed.

Walking up and down the stairs is a wise exercise to burn calories. Approximately 300 calories may be burned by walking the stairs for about 30 minutes. Doesn't which sound like a considerable big calories burned calculator number? However, it surely is a lot of difficult function.

Many people find it difficult to get rid of weight because they have no idea how many calories they consume during the day and how various calories they burn off. A calories burned calculator could assist them keep track of the amount of calories they are burning throughout the day. We burn off calories throughout the day by usual escapades. Walking up and down the stairs or really walking in the park are two simple techniques which we burn calories. We even burn calories whenever you may be sleeping. Using a calorie burn calculator offers you a wise decision of how numerous calories you may be burning off each day.

Do you today see the difference between 113 calories and 180 calories? If that girl spends 5 hours a week in that aerobics class, the standard calorie counters may overreport her calorie output by: (180-113) * 10 = 670 calories a week. The girl is misled which her metabolic rate has dropped while she only overestimated her calorie expenditure. Enter fat loss plateau, wasted time plus efforts. Do we have the time for trial and error calorie estimations?

Are you seeking an HONEST and ALL-NATURAL Diet & Nutrition Program to by finding the best fat burning foods? Visit The Diet Solution Program for tons of Tips and Tricks! Stop DietingStart Eatingand Start Living! http://thedietsolutionprogram.com.

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