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Re: ((a&&b)||c)==((a||c)&&(b||c))

On 9 Nov 2005, at 17:45, Steven T. Hatton wrote:

> Why does Mathematica not determine that the following is true?
> ((a \[And] b) \[Or] c) == ((a \[Or] c) \[And] (b \[Or] c))
> This little function shows that the lhs  and rhs have the same  
> truth tables,
> and are therefore equivalent:
> TruthTable[s_, argc_] := Module[
>     {tt = Tuples[{True, False}, argc]},
>     {#, s @@ #} & /@ tt // TableForm
>     ]
> -- 
> The Mathematica Wiki:
> Math for Comp Sci
> Math for the WWW:

Because, (as I tried to explain in a reply to a recent posting of  
yours) this is not the way == is used in Mathematica. The correct way  
to show this is:

Implies[(a â?¨ c) â?§ (b â?¨ c),(a â?§ b) â?¨ c]//FullSimplify


Implies[(a â?§ b) â?¨ c,(a â?¨ c) â?§ (b â?¨ c)]//FullSimplify


Andrzej Kozlowski

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