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!