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→Logical Equivalence Problem: list FUT's
===Solution===
===Solution===
[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].
In logical graphs, the required equivalence looks like this:
In logical graphs, the required equivalence looks like this:
</pre>
</pre>
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]].
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:
:* [[Logical_graph#Axioms|Logical Graph Axioms]]
:* [[Logical_graph#Axioms|Logical Graph Axioms]]
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:
:* [[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]]