       Re: Inequalities

• To: mathgroup at smc.vnet.net
• Subject: [mg69699] Re: Inequalities
• From: "Dana DeLouis" <dana.del at gmail.com>
• Date: Thu, 21 Sep 2006 07:29:28 -0400 (EDT)

```>It should be, if 1 - q > p.

Hello.  Reduce seems to suggest there are two areas.

equ = p*(1 - p) < q*(1 - q);

FullSimplify[Assuming[0 < p < q < 1, Reduce[equ, {p, q}]]]

(p > 1/2 && p + q > 1 && p > q) || (p < 1/2 && p + q < 1 && p < q)

I wasn't sure about the 1/2 part.
However, the plot below seems to suggest it is correct.
If I'm not mistaken, the white area represents "True."

ContourPlot[Boole[equ], {p, -3, 3}, {q, -3, 3}, Contours -> 1,
Axes -> True, PlotPoints -> 300, RotateLabel -> False,
FrameLabel -> {"\n p", "q"}, PlotLabel ->
"\n White Area is True \n"];

HTH
Dana DeLouis
Mathematica 5.2
dana.del at gmail.com

>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!

```

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