# Thread: A very annoying and simple logic derivation problem.

1. ## 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.

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.

2. Well we do know the $\neg A \vee B \equiv A \to B \equiv \neg B \to \neg A$.

3. 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?

4. 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.

5. 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).