Author 
Comment/Response 
David

08/20/10 05:01am
Hello!
I'm trying to get solution for x and y in the following system using Mathematica 7.
(1) x  A >= y  A iff 0 <= A <= 1/2
(2) x  A < y  A iff 1/2 < A <= 1
where 0 <= x <= 1 and 0 <= y <= 1.
I'm solving for reals.
I’ve rewritten this problem and asked Mathematica. This is the code:
Resolve[
Exists[{x,y},0<=x<=1&&0<=y<=1,
ForAll[{A,B},1/2<A<=1&&0<=B<=1/2,
Abs[xA]< Abs[yA]&&Abs[xB]>=Abs[yB]
]
]
]
Which yields True, but I’d like to get a straight answer  for which x and y is this true.
Note I used two parameters, A and B, because you cannot expect A<=1/2 and 1/2<A to hold true at the same time.
(I guessed one solution, which is 1 and 0 for x and y respectively.)
Any ideas? Thanks to anyone trying to help!
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