# question on notion of 'proves'...

• Apr 24th 2010, 08:36 AM
NYC
question on notion of 'proves'...
Is it possibe to have
A proves B
and
not A proves B

I'm tending towards thinking you can't, but not sure why. Any ideas?
• Apr 24th 2010, 09:51 AM
oldguynewstudent
Quote:

Originally Posted by NYC
Is it possibe to have
A proves B
and
not A proves B

I'm tending towards thinking you can't, but not sure why. Any ideas?

I'm not sure what you mean by "proves". If you mean implies then the answer is yes.

p q p-->q

T T T
T F F
F T T
F F T
• Apr 24th 2010, 10:04 AM
PiperAlpha167
Quote:

Originally Posted by NYC
Is it possibe to have
A proves B
and
not A proves B

I'm tending towards thinking you can't, but not sure why. Any ideas?

But here's a valid sequent you might consider.

A->B, ~A->B |- B or alternatively,

|- (A->B) -> ((~A->B) -> B),

or getting conjunction into the "equation",

|- ((A->B) & (~A->B)) -> B
• Apr 24th 2010, 12:53 PM
emakarov
Quote:

Is it possibe to have
A proves B
and
not A proves B
This is possible iff B is provable by itself.
• Apr 25th 2010, 12:09 PM
NYC
Quote:

Originally Posted by emakarov
This is possible iff B is provable by itself.

Thanks
In this case is B a tautology?
• Apr 25th 2010, 12:22 PM
oldguynewstudent
Quote:

Originally Posted by NYC
Thanks
In this case is B a tautology?

You betcha!
• Apr 25th 2010, 12:25 PM
NYC
Quote:

Originally Posted by oldguynewstudent
You betcha!

Thanks for the quick response!
How would you show that B is a tautology?
• Apr 25th 2010, 01:24 PM
oldguynewstudent
Quote:

Originally Posted by NYC
Thanks for the quick response!
How would you show that B is a tautology?

That would depend on B. Do you have the example of your actual problem?