Re: Derivations

1st Semester Logic Student wrote:
> Hey all,
>
> We have recently moved on to the wonderful world of "derivations." :P I
> have found that there is more than one way to derive a sentence in SL
> from the premis. How would you guys go about showing that the following
> derviation claims hold in SD?

Do you know what 'SD' stands for? That might be a start.

Thanks.

Ken

> Obviously we need to construct a
> derivation. How can I type my derivations on the message board? The
> following are the ones I'm working on now. Any advice on the best ways
> of deriving the following would be helpful as well as any tactics that
> may be the best. I have read of a way to work backwards, but I stink at
> that so far, so I'm just working from the premis down to what it is I'm
> trying to derive.
>
> a) {A v B, ~B} single-turnstile A
> b) {[A horseshoe (~B horseshoe C)], A & ~B} single-turnstile C v E
> c) {(~A v ~B) horseshoe C, D & ~C} single-turnstile A
> d) {A horseshoe ~~B, C horseshoe ~B} single-tunrstile ~(A & C)
>
> Now, in the above I wrote out some of the symbols (horseshoe and
> single-turnstile) so that everyone would be able to read it. Please
> forgive my "noobieness." Obviously everything before the
> single-turnstile are the main assumptions and after the turnstile is
> the conclusion which is what I'm trying to derive.
>
> I have some others that I'm trying to show are a theorem in SD. I am
> doing this by deriving them from an empty set. This part confuses me
> more than the above. Some of these problems are the following:
>
> e) A horseshoe (B horseshoe A)
> f) ~A horseshoe ((B & A) horseshoe C)
> g) (A v B) horseshoe (B v A)
> h) A tripplebar ~~A
>
> Any answers, advice, help, suggestions? I have some truth tables to
> work on as well, but they seem very straight forward and I don't think
> I need any help with those. I may type up the questions and what I got
> as answers just to let you guys check my work.
>
> Thanks!
> Logic Noob

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