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

• To: mathgroup at smc.vnet.net
• Subject: [mg62015] ((a&&b)||c)==((a||c)&&(b||c))
• From: "Steven T. Hatton" <hattons at globalsymmetry.com>
• Date: Wed, 9 Nov 2005 03:45:29 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

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: http://www.mathematica-users.org/
Math for Comp Sci http://www.ifi.unizh.ch/math/bmwcs/master.html
Math for the WWW: http://www.w3.org/Math/

• Follow-Ups:
  • Re: ((a&&b)||c)==((a||c)&&(b||c))
    • From: Daniel Lichtblau <danl@wolfram.com>
  • Re: ((a&&b)||c)==((a||c)&&(b||c))
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>