Re: logical simplification problem

• To: mathgroup at smc.vnet.net
• Subject: [mg101505] Re: logical simplification problem
• From: olfa <olfa.mraihi at yahoo.fr>
• Date: Thu, 9 Jul 2009 01:53:56 -0400 (EDT)
• References: <200907071147.HAA27538@smc.vnet.net> <h31uj8\$bi0\$1@smc.vnet.net>

```On 8 juil, 13:06, Daniel Lichtblau <d... at wolfram.com> wrote:
> olfa wrote:
> > Hi mathematica community,
> > if it does not exist as predefined function in mathematica, how to
> > define a rule that illustrate this logical property: if p implies q
> > then p || q is simplified into q and p&&q is simplified into p?
> > Thank you for your help.
>
> Possibly you are looking for BooleanMinimize.
>
> In[15]:= BooleanMinimize[{p || q, p && q}, "DNF", Implies[p, q]]
>
> Out[15]= {q, p}
>
> Daniel Lichtblau
> Wolfram Research

Thank you very much for your reply Mr Daniel and thank you for each
one who take the time to answer my question.
In fact, The function BooleanMinimize seems to do what I want but the
problem now is that Implies doesn't test if p implies q is really true
or false . I want to use something like ImpliesQ (which unfortunately
become obsolete) in order to test the implication and so if it is true
the expression is minimized and if it is false it stills in the same
form.
Any suggestion?

```

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