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==Majority Function Example==
==Majority Function Example 1.0==
===Proof 1 : Storyboard===
===Proof 1 : Storyboard===
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| [[Image:Majority Function 600 x 300 Animation.gif]]
| [[Image:Majority Function 600 x 300 Animation.gif]]
|}
==Majority Function Example 2.0==
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].
{| align="center" cellpadding="10"
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<math>\begin{matrix}
a b \bar{c} + a \bar{b} c + \bar{a} b c + a b c
\\[6pt]
\iff
\\[6pt]
a b + a c + b c
\end{matrix}</math>
|}
===Proof 1 : Storyboard===
{| align="center" cellpadding="0" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center"
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| [[Image:Majority Function Example Proof 1 Title.jpg|500px]]
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| [[Image:Majority Function Example 2.0 Proof 1 Frame 1.jpg|500px]]
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| [[Image:Equational Inference Reflect ab, ac, bc.jpg|500px]]
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| [[Image:Majority Function Example 2.0 Proof 1 Frame 2.jpg|500px]]
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| [[Image:Equational Inference Distribute (abc).jpg|500px]]
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| [[Image:Majority Function Example 2.0 Proof 1 Frame 3.jpg|500px]]
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| [[Image:Equational Inference Collect ab, ac, bc.jpg|500px]]
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| [[Image:Majority Function Example 2.0 Proof 1 Frame 4.jpg|500px]]
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| [[Image:Equational Inference Quit (a), (b), (c).jpg|500px]]
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| [[Image:Majority Function Example 2.0 Proof 1 Frame 5.jpg|500px]]
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| [[Image:Equational Inference Cancel (( )).jpg|500px]]
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| [[Image:Majority Function Example 2.0 Proof 1 Frame 6.jpg|500px]]
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| [[Image:Equational Inference Weed ab, ac, bc.jpg|500px]]
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| [[Image:Majority Function Example 2.0 Proof 1 Frame 7.jpg|500px]]
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| [[Image:Equational Inference Delete a, b, c.jpg|500px]]
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| [[Image:Majority Function Example 2.0 Proof 1 Frame 8.jpg|500px]]
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| [[Image:Equational Inference Cancel (( )).jpg|500px]]
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| [[Image:Majority Function Example 2.0 Proof 1 Frame 9.jpg|500px]]
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| [[Image:Equational Inference QED.jpg|500px]]
|}
===Proof 1 : Animation===
Here's an animated recap of the graphical transformations that occur in the above proof:
{| align="center" cellpadding="0" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center"
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| [[Image:Majority Function Example 2.0 Animation.gif]]
|}
|}