Logical Converses

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Timefly
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Logical Converses

Postby Timefly » Sat Dec 10, 2011 4:33 pm UTC

Given that I have a conjecture and if that conjecture were to be proved true it would show that a certain set of equations could not exist.
If I could prove that said set of equations didn't exist by other means, could I then use that result yo somehow show that the conjecture is true?

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jestingrabbit
Factoids are just Datas that haven't grown up yet
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Re: Logical Converses

Postby jestingrabbit » Sat Dec 10, 2011 5:08 pm UTC

No. You would have (A-> B) AND (C->B). A=F, B=T and C=T satisfies the expression ie your conjecture could be false and the conclusion true. You need to demonstrate that the conjection is true iff the equations don't exist, or some other condition that implies the conjecture to prove the conjecture. That the conjecture implies something and that something is true is nice, and at least gives you reason for hope, but turning it into a proof would require something else.
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Timefly
Posts: 56
Joined: Sun Nov 14, 2010 7:30 pm UTC

Re: Logical Converses

Postby Timefly » Sat Dec 10, 2011 6:02 pm UTC

Thanks, this is really useful. I think I just realized how I might be able to show that the conjecture relies on the equations existing. me thinks this shall not be simple though.

tomtom2357
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Re: Logical Converses

Postby tomtom2357 » Sat Dec 31, 2011 8:53 am UTC

I'm interested, what conjecture are you studying?
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.


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