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Directory:Jon Awbrey/Papers/Propositional Equation Reasoning Systems (view source)

Revision as of 19:40, 24 March 2010

82 bytes added ,  19:40, 24 March 2010
→‎Exemplary proofs: renumb figs
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| [[Image:PERS_Figure_12.jpg|500px]] || (12)
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| [[Image:PERS_Figure_12.jpg|500px]] || (α)
 
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| [[Image:PERS_Figure_13.jpg|500px]] || (13)
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| [[Image:PERS_Figure_13.jpg|500px]] || (β)
 
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| [[Image:PERS_Figure_15.jpg|500px]] || (15)
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| [[Image:PERS_Figure_15.jpg|500px]] || (β)
 
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====Majority function example====
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====Two-thirds majority function====
    
Consider the following equation in boolean algebra, posted as a [http://mathoverflow.net/questions/9292/newbie-boolean-algebra-question problem for proof] at [http://mathoverflow.net/ MathOverFlow].
 
Consider the following equation in boolean algebra, posted as a [http://mathoverflow.net/questions/9292/newbie-boolean-algebra-question problem for proof] at [http://mathoverflow.net/ MathOverFlow].
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<math>\begin{matrix}
 
<math>\begin{matrix}
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a b + a c + b c
 
a b + a c + b c
 
\end{matrix}</math>
 
\end{matrix}</math>
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| (&alpha;)
 
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=====Proof 1 : Storyboard=====
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The required equation can be proven in the medium of logical graphs as shown in the following Figure.
    
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| [[Image:Equational Inference QED.jpg|500px]]
 
| [[Image:Equational Inference QED.jpg|500px]]
 
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| (16)
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| (&beta;)
 
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=====Proof 1 : Animation=====
      
Here's an animated recap of the graphical transformations that occur in the above proof:
 
Here's an animated recap of the graphical transformations that occur in the above proof:
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| [[Image:Majority Function Example 2.0 Animation.gif]]
 
| [[Image:Majority Function Example 2.0 Animation.gif]]
 
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| (17)
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| (&gamma;)
 
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Jon Awbrey
12,140

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