Deductive Symbolic Logic needed please (solving a proof)

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  3. » Deductive Symbolic Logic needed please (solving a proof)

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Reply Tue 19 May, 2009 09:41 am

I have tried working this proof for at least 4 hours now. I'm not sure what I am doing wrong, I think I am missapplying the rules for the "~"/"not" values?:brickwall: (this emoticon is perfect!! LOL)

I need to use inference and replacement rules as well as Indirect Proof method to solve. I start with supposing ~(A->~E) and go from there.

= stands for "if and only if" (triple bar)
~ stands for negation
v stands for disjunction "or"
& stands for conjunction "and"
-> stands for "if....then" (horseshoe)

~(A v B) v ~(C v D)
(E v F) -> D

A -> ~E

I just keep going round and round with this! I will be online checking my messages if anyone has some questions for me about this. Thank You
Reply Tue 19 May, 2009 01:48 pm
Hi jwass52!

The proof is difficult in the respect that it does not give you an open variable to work with, so I can definitely understand your frustration with it. I found it easier to do it under a conditional proof with a single indention. You could do it in a few less steps if you use a few nested proofs, but that ends up overcomplicating it and I don't know if you can use them or not for your class (assuming you are taking one for logic.) For this particular proof it is probably best to use a conditional proof rather than an indirect proof. This is not to say that indirect proof is not possible, in fact it may actually be a little bit easier but I find conditional proofs little easier to use especially considering the conclusion in this proof.

If you have any questions, just let me know, I'm happy to help out in any way I can.
Victor Eremita
Reply Tue 19 May, 2009 03:32 pm
I love doing indirect proofs

Here is the solution for that
1. ~(A v B) v ~(C v D)
2. (E v F) -> D
A -> ~E
3. ~(A -> ~E) (Assumption)
4. ~(~A V ~E) (Implication, 3)
5. A ^ E (De Morgans, 4)
6. E (Simplifcation, 5)
7. E V F (Addition, 6)
8. D (MP 2, 7)
9. A (Simplifcation, 5)
10. A V B (Addition, 9)
11. ~(C V D) (DS, 1, 11)
12. ~C ^ ~D (De Morgan's 11)
13. ~D (Simplifcation, 12)
14. D ^ ~D (Conjuction 8, 13)
A -> ~E

Vid, do you use Paint for that or a specialized program?
Reply Tue 19 May, 2009 05:12 pm
I usually use paint to do the examples that I do. With paint, I have been able to get the right size where the picture does not get resized becuase of the restrictions on the forum. But the next time I do a proof I am going to try to use photoshop because all I have to do is make a proof template and insert the elements into the proof. I have one program from one of my logic books (Prospesel)that lets you input everything and it then formulates the format for you, but it is not really as good as doing it by hand.
Reply Tue 19 May, 2009 05:13 pm
@Victor Eremita,
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