# Basic SL proof using DS

#### debiant

I am reading Logic for Dummies... and that should probably end my question answer and existence, but there is a proof in the book that is giving me fits. I've searched

Code:
P -> ~Q, P V R, Q V S, ~R: ~P V S

1. P -> ~Q      P
2. P V R        P
3. Q V S        P
4. ~R           P
5. P            2, DS
6. ~Q           1, 5, MP
7. S            3, 6, DS
8. ~P V S       7, ADD
The conclusion is what makes no sense to me. How can you go from P to ~P. Is this a typo in the book, or am I missing something?

Thanks.

I'm going to switch to another book because this is a little to kitschy for me, but I would like to find out if my logic is flawed.

#### undefined

MHF Hall of Honor
I am reading Logic for Dummies... and that should probably end my question answer and existence, but there is a proof in the book that is giving me fits. I've searched

Code:
P -> ~Q, P V R, Q V S, ~R: ~P V S

1. P -> ~Q      P
2. P V R        P
3. Q V S        P
4. ~R           P
5. P            2, DS
6. ~Q           1, 5, MP
7. S            3, 6, DS
8. ~P V S       7, ADD
The conclusion is what makes no sense to me. How can you go from P to ~P. Is this a typo in the book, or am I missing something?

Thanks.

I'm going to switch to another book because this is a little to kitschy for me, but I would like to find out if my logic is flawed.
If S is true then X V S is true no matter what X is.

My statement: "The moon is made of cheese" OR "The sky is blue."

Assuming that the sky is in fact blue, then my statement is true even though the moon is clearly not made of cheese. (Or is it?)