Sentential Logic Problem - Proving Truth: Philosophy Forums

Sentential Logic Problem - Proving Truth

slyboots
Initiate

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Posted 03/16/08 - 10:48 PM: Subject: Sentential Logic Problem - Proving Truth	#1
Hey everyone, trying to get a handle on this problem and I'm stumped as to where to go. Not sure if I'm headin in the right direction or not. Any help is much appreciated. "Prove the following claim is true in SD+" { A⊃(F v E) , (~B & D) v (~A⊃C) , ~(C v F) & [(F v ~E)≡A] } models B≡~E ***For some reason models isnt working.. what I mean to say is that B≡~E is derivable from the aforementioned set. THANKS!

MoeBlee
aka I. Kabruob

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Posted 03/17/08 - 03:38 PM:	#2
I don't know the specifics of SD+, but I can you give you some correct reasoning, not necessarily confined to a particualar system. Then perhaps you can fill in any details you need for your particular system. (But I don't know why you say 'models' as opposed to 'proves'.) Suppose A -> (F v E) (~B & D) v (~A -> C) ~(C v F) & ((F v ~E) <-> A) Show: B <-> ~E Suppose B. So ~(~B & D). So ~A -> C. So ~C -> A. But ~C. So A. So F v ~E. But ~F. So ~E. So B -> ~E. Suppose ~E. So F v ~E. So A. So F v E. So F. But ~F. Contradiction. So any conclusion, specifically B. So ~E -> B. So B <-> ~E.

The Bearded Monkey
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Posted 03/17/08 - 10:45 PM:	#3
You should point there why but ~C,but ~F in the first lines, obviously they follow from the last proposition given in the question.
_____________________ i shall take the whichpath to quantum catastrophe theory.

MoeBlee
aka I. Kabruob

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Posted 03/18/08 - 09:42 AM:	#4
~C comes from ~(C v F). ~F comes from ~(C v F).

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