MyWikiBiz, Author Your Legacy — Thursday November 14, 2024
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, 20:50, 3 December 2008
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| ===Solution=== | | ===Solution=== |
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− | [http://mathforum.org/kb/plaintext.jspa?messageID=6514666 Solution posted by Jon Awbrey, worked out in terms of logical graphs]. | + | [http://mathforum.org/kb/plaintext.jspa?messageID=6514666 Solution posted by Jon Awbrey, using the calculus of logical graphs]. |
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| In logical graphs, the required equivalence looks like this: | | In logical graphs, the required equivalence looks like this: |
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| </pre> | | </pre> |
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− | See [http://www.mywikibiz.com/Logical_graph#C2.__Generation_theorem Logical Graph : C<sub>2</sub>. Generation Theorem]. | + | See [[Logical_graph#C2.__Generation_theorem|Logical Graph : C<sub>2</sub>. Generation Theorem]]. |
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| Applying this twice to the left hand side of the required equation, we get: | | Applying this twice to the left hand side of the required equation, we get: |
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| :* [[Logical_graph#Axioms|Logical Graph Axioms]] | | :* [[Logical_graph#Axioms|Logical Graph Axioms]] |
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− | Proceeding from these axioms is a handful of very simple theorems that we tend to use over and over in deriving more complex theorems. A sample of these is given here: | + | Proceeding from these axioms is a handful of very simple theorems that we tend to use over and over in deriving more complex theorems. A sample of these frequently used theorems is given here: |
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− | :* [[Logical_graph#Frequently_used_theorems|Frequently Used Theorems]] | + | :* [[Logical_graph#C1.__Double_negation_theorem|C<sub>1</sub>. Double Negation Theorem]] |
| + | :* [[Logical_graph#C2.__Generation_theorem|C<sub>2</sub>. Generation Theorem]] |
| + | :* [[Logical_graph#C3.__Dominant_form_theorem|C<sub>3</sub>. Dominant Form Theorem]] |