Re: Need help with a simple logic proof.

On Fri, 09 Mar 2007 01:16:20 -0500, herbzet <herbzet@xxxxxxxxx> wrote:


I've tried everything I can think of, I just can't get this conclusion
from these premises. Here's theproblem:

1. L->M
2. N->O
C. L v N -> M v O

Here's a proof in some standard system of natural deduction.

1 (1) L -> M A
2 (2) N -> O A
3 (3) L v N A
4 (4) L A (first disjunct of L v N)
1,4 (5) M 1,4 ->E (MP)
1,4 (6) M v O 5 vI
7 (7) N A (second disjunct of L v N)
2,7 (8) O 2,7 ->E (MP)
2,7 (9) M v O 8 vI
1,2,3 (10) M v O 3,4,6,7,9 vE
1,2 (11) L v N -> M v O 3,10 ->I (CP)

Thanks a lot for the help. Unfortunately for this problem we weren't
allowed to use conditional proofs or indirect proofs, but I think I
have an idea for solving it using conjunction and distribution.

If you come up with a nice proof, please post it. My first run
at it I came up with

1. L -> M
2. N -> O
3. (L -> M) & (N -> O) (addition?)

is equal to

(~L & ~N) v (M & ~N) v (~L & O) v (M & 0)

but that's as far as I got.

Yeah, I also tried this line of thought. But it seems that it leads to
nowhere.

Problem is, that the OP seems to have to use one of Copi's ugly systems of
"natural deduction" (or a descendant of one of his systems). So it's hard
to say which rules are allowed and which are not. Actually, I simply don't
remember all those rules, not even of ONE of his (various) systems. :-(

The OP wrote:

"[Allowed rules are:] modus ponens, modus tollens, hypothetical syllogism,
disjunctive syllogism, constructive dilemma, conjunction, simplification,
addition, transposition, material implication, material equivalence,
exportation, tautology, De Morgan's theorem, computation, association,
distribution, and double negation."

!!! sigh !!!


F.


P.S.
But I guess the mentioned rules might allow to formulate the following
argument as a proof:

L -> M => L -> M v O
N -> 0 => N -> M v O ??? (See below.)

N -> O => N -> O v M.
O v M -> M v O
(N -> O v M) -> ((O v M -> M v O) -> (N -> M v O))
=> => N -> M v O.

(L -> M v O) -> ((N -> M v O) -> (L v N -> M v O))
=> => L v N -> M v O.

--

E-mail: info<at>simple-line<dot>de
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