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logic: proof problem

 
 
Sasqi
 
Reply Fri 19 Mar, 2010 09:09 am
Translate into symbolic form without quantification and provide a non-conditional proof for the
following argument:

Credit markets will function properly and the stock market will recover, if and only if the Obama financial recovery plan works. If credit markets function properly, the stock market will recover. Therefore, credit markets will function proprrty if and only if the Obama financial recovery plan works.

For the symbolic form, I got:
[(A?B)⊃C]?[C⊃(A?B)]
A⊃B
therefore: (A⊃C)?(C⊃A)

As for (my attempt at) the proof:

1 [(A?B)⊃C]?[C⊃(A?B)]
2 A⊃B
therefore: (A⊃C)?(C⊃A)
3 (A?B)⊃C simp.1
4 C⊃(A?B) simp.1
5 ?(A?B)∨C M.I. 3
6 ?C∨(A?B) M.I. 4
7 (?C∨A)?(?C∨B) Dist.6
8 C∨?(A?B) Com. 6
9 C∨(?A∨?B)
10 ?C∨A Simp.7
11 ?C∨B Simp.7
12 C⊃A M.I.10
13 A⊃(B⊃C) Exp.3

it's due in about an hour:P so any help would be greatly appreciated! thanks:)
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Doubt doubt
 
  1  
Reply Fri 19 Mar, 2010 09:43 am
@Sasqi,
Seems fallacious via over simplification to me. seems like the math would need to account for the random things that will happen. but i guess the argument itself doesnt matter, just the abstract math being applied to the objective world. Somehow this can be seen as useful even without the infinite variables accounted for?
0 Replies
 
Emil
 
  1  
Reply Fri 19 Mar, 2010 11:42 am
@Sasqi,
Sasqi;141244 wrote:
Translate into symbolic form without quantification and provide a non-conditional proof for the
following argument:

Credit markets will function properly and the stock market will recover, if and only if the Obama financial recovery plan works. If credit markets function properly, the stock market will recover. Therefore, credit markets will function proprrty if and only if the Obama financial recovery plan works.

For the symbolic form, I got:
[(A?B)⊃C]?[C⊃(A?B)]
A⊃B
therefore: (A⊃C)?(C⊃A)

As for (my attempt at) the proof:

1 [(A?B)⊃C]?[C⊃(A?B)]
2 A⊃B
therefore: (A⊃C)?(C⊃A)
3 (A?B)⊃C simp.1
4 C⊃(A?B) simp.1
5 ?(A?B)∨C M.I. 3
6 ?C∨(A?B) M.I. 4
7 (?C∨A)?(?C∨B) Dist.6
8 C∨?(A?B) Com. 6
9 C∨(?A∨?B)
10 ?C∨A Simp.7
11 ?C∨B Simp.7
12 C⊃A M.I.10
13 A⊃(B⊃C) Exp.3

it's due in about an hour:P so any help would be greatly appreciated! thanks:)


I wrote a long answer but my computer crashed and I cannot be bothered to write it again. I did a check of the argument using truth tables, and it is valid (if I did the table correctly).

http://img209.imageshack.us/img209/1659/truthtableproof.jpg
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