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Re: Inequalities

• To: mathgroup at smc.vnet.net
• Subject: [mg69713] Re: [mg69660] Inequalities
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Thu, 21 Sep 2006 07:30:35 -0400 (EDT)

On 20 Sep 2006, at 15:44, misha wrote:

> I am an inexperienced user and am wondering whether Mathematica can  
> help
> me with inequalities such as the following.
>
> Given 0 < p < q < 1,
>
> When is p(1-p)<q(1-q)?
>
> It should be, if 1 - q > p.
>
> Thanks!
>


For example,


Simplify[Reduce[{p*(1 - p) < q*(1 - q), 0 < p < q < 1},
    {p, q}], {0 < p < q < 1}]


p < 1/2 && p + q < 1

Andrzej Kozlowski

Tokyo, Japan