# A very annoying and simple logic derivation problem.

• Jan 14th 2009, 03:34 PM
Freols
A very annoying and simple logic derivation problem.
Hello everyone!

Right, I know I'm overlooking something really simple here, and it frustrates me a lot. :D

My primary assumption is:

~A v B

and I want to derive:

A ⊃B

I started of with a sub-goal analysis method, then got stumped fairly quickly.
I then tried to start from the top top...
In short, what can you derive from '~A v B'? As far as I know, without any other information you can't derive anything at all... but to solve this derivation, surely you must derive something from it?

It seems like it should be such a simple derivation as well, what am I ignorantly missing?

Thanks a bunch chaps. (Itwasntme)
• Jan 14th 2009, 03:41 PM
Plato
Well we do know the $\neg A \vee B \equiv A \to B \equiv \neg B \to \neg A$.
• Jan 14th 2009, 03:56 PM
Freols
Thanks for the fast reply Plato.

I'm afraid I only know Sentential Logic, and unless it's written out in a way I haven't yet seen, I don't think that's SL. I'm still confused as to what the first step would be... disjunction elimination? Biconditional introduction?
• Jan 14th 2009, 04:09 PM
Plato
Quote:

Originally Posted by Freols
I'm afraid I only know Sentential Logic, and unless it's written out in a way I haven't yet seen, I don't think that's SL. I'm still confused as to what the first step would be... disjunction elimination? Biconditional introduction?

The statement that not A or B is equivalent to A implies B is equivalent to not B implies not A.
The proofs of these are most easily done with truth tables.
I guess that I really do not know exactly what you are asking notwithstanding having taught logic for years.
• Jan 14th 2009, 09:01 PM
alglogic
not quite sure if this is the kind of thing you are looking for, but with the premise -A or B, one can prove A -> B via the conditional introduction rule. Thus when you assume A, this implies --A (via some sort of double negation rule), and this in turn implies B (via your initial premise and a disjunction-elimination rule).