Checking whether statement A implies statement B

Question

I would like to ask Mathematica "does statement A imply statement B?" and get a yes or no (true or false) answer whenever one exists.

I have entered the input Reduce[ Implies[x>0 && y>0 , xy > 0] ]. The output I was expecting was true. The output I actually get is x <= 0 || y <= 0 || (y < 0 && x < 0) || (y > 0 && x > 0).

Could someone explain how I can get Mathematica to produce the desired result from the first paragraph?

Specifying Reals as domain seems to do the trick for dome reason — Lukas Lang, Jul 05 '18 at 10:43

score 4 · Accepted Answer · answered Jul 05 '18 at 13:26

4

Mind the space between x and y!

Simplify@Reduce[
  Implies[x > 0 && y > 0, x y > 0]
  , {x, y}
  ]

True

answered Jul 05 '18 at 13:26

rhermans

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The lack of a space in my question was a typo (I had one in my Mathematica notebook). But it's the Simplify that indeed makes the difference. I'm embarrassed I didn't think of this. Thanks. – Ubiquitous Jul 05 '18 at 13:56

Checking whether statement A implies statement B

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