Re: Logic Proofs

On Mon, 05 Dec 2005 03:50:35 EST, Mikey <mrpoopypants_tres@xxxxxxxxx>
wrote:

Solutions are rather straight forward:
>
> 1. ~A > [~B > (C > B)]
> 2. A v ~B
> 3. ~A /~C
>

(1) ~A -> (~B -> (C -> B)) Premise
(2) A v ~B Premise
(3) ~A Premise
(4) ~B -> (C -> B) MP 1,3
(5) ~B DS 2,3
(6) C -> B MP 4,5
(7) ~C MT 6,5

>
> 1. (P * Q) > (R v S)
> 2. (~R v L) > P
> 3. (~R v M) > Q
> 4. ~R * T /S
>

(1) (P & Q) -> (R v S) Premise
(2) (~R v L) -> P Premise
(3) (~R v M) -> Q Premise
(4) ~R & T Premise
(5) ~R Simp. 4
(6) ~R v L Add. 5
(7) ~R v M Add. 5
(8) P MP 2,6
(9) Q MP 3,7
(10) P & Q Conj. 8,9
(11) R v S MP 1,10
(12) S DS 11,5

>
> 1. ~(~A * ~B) > C
> 2. D > (B v A) /D > C

(1) ~(~A & ~B) -> C Premise
(2) D -> (B v A) Premise
(3) D -> (A v B) Com. 2
(4) D -> ~~(A v B) DN 3
(5) D -> ~(~A & ~B) DeM 4
(6) D -> C HS 5,1


This one is slightly more complicated:
>
> 1. (L > M) * (N > M)
> 2. L v P
> 3. N v ~P /M
>

(1) (L -> M) & (N -> M) Premise
(2) L v P Premise
(3) N v ~P Premise
(4) L -> M Simp. 1
(5) N -> M Simp. 2
:

The rest of the proof is left as an exercise for the reader.


X.
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