Comparing result sets from Reduce in Mathematica

Questions
1

Hi,

Is there a simple way to check whether two result sets are equivalent/the same?

Here’s a toy example:

A = x>0;
B = -x<0;

I’d like to test if A==B. For example, this command outputs

(x > 0) == (-x < 0).

I’ve also tried using Complement, with no success.

Thank you!
Pedro

2

The best way to handle inequalities is to treat them as logic statements and use Resolve:

A = x > 0; B = -x < 0;

Resolve[ForAll[x, Equivalent[A, B]], Reals]

True

Strictly speaking, depending on what you mean by “Set”, it might be impossible to write an algorithm in any programming language that guarantee whether two sets are the same or not.

3

Sean,

This is exactly what I was looking for; it does work for “simple” cases.

Thanks!
P