Intro Logic Proof Help Wanted: Philosophy Forums

Intro Logic Proof Help Wanted

logicprincess
Initiate

Usergroup: Members
Joined: Apr 08, 2008
Total Topics: 1
Total Posts: 2

Posted 04/08/08 - 06:23 PM: Subject: Intro Logic Proof Help Wanted	#1
So here is the homework problem that I have: 1. C --> (D v ~E) 2. E --> (D --> F) // C --> (E --> F) I am supposed to use condition proof and the eighteen rules of inference to get to the conclusion. What I have is: 3. C ACP 4. D v ~E 1, 3 MP 5. ~E v D 4, Com 6. E --> D 5, Impl. That's about as far as I get. I can envision using HS to get (E --> F) on a line by itself. E --> D is right there. If I can get E on a line by itself that I can MP the (D --> F) on a line by itself and then HS to my goal in the conditional proof. But I am uncertain as to how to get there. I also see potential to use CD. C v E Add [C --> (D v ~E)] & [E --> (D --> F)] (D v ~E) v (D --> F) Please help! I would like to figure this out in the next hour. It's the last problem for this homework set.

7
Graduate

Usergroup: Members
Joined: Mar 23, 2008
Total Topics: 3
Total Posts: 160

Posted 04/09/08 - 05:32 AM:	#2
1. C --> (D v ~E) 2. E --> (D --> F) // C --> (E --> F) 3. C ; ACP 4. (E ^ D) -> F ; 2 Exp 5. D v ~E ; 1,3 MP 6. ~E v D ; 5 Com. 7. E -> D ; 6 Imp 8. E -> (E ^ D) ; 7 Abs 9. E -> F ; 4,8 HS 10. C -> (E - F) ; CP QED

logicprincess
Initiate

Usergroup: Members
Joined: Apr 08, 2008
Total Topics: 1
Total Posts: 2

Posted 04/11/08 - 08:26 AM:	#3
What is the rule Abs? Sorry, but I don't think we use that one in class. It looks useful though. Thanks for the help. I hope that more questions from me will be welcome here.

Brian Bosse
Aspirant

Usergroup: Members
Joined: Mar 29, 2008
Total Topics: 2
Total Posts: 22

Posted 04/11/08 - 09:30 AM:	#4
Hello LogicPrincess, What is the rule Abs? Sorry, but I don't think we use that one in class. I, too, am not sure what is meant by this. However, the logic is straightforward. Step 6 shows that E --> D. We also know that E --> E. Therefore, E implies both D and E. Here would be one derivation of this... 1. E --> D 2. ~~Show~~ E --> E ----------3. Assume E ----------4. E [repeat - 3] (Step 2 is now shown) 5. ~~Show~~ E --> (E ^ D) ----------6. Assume E ----------7. D [Modus Ponens - 1, 6] ----------8. E [Modus Ponens - 2, 6] ----------9. (E ^D) [Adjunction - 7, 8] (Step 5 is now shown) My guess is that 7's 'Abs' is meant to be a short cut reference to the above derivation. Sincerely, Brian

7
Graduate

Usergroup: Members
Joined: Mar 23, 2008
Total Topics: 3
Total Posts: 160

Posted 04/11/08 - 11:36 AM:	#5
logicprincess wrote: What is the rule Abs? Sorry, but I don't think we use that one in class. It looks useful though. Thanks for the help. I hope that more questions from me will be welcome here. 'Abs.' is absorption. From p -> q infer p -> (p ^ q). http://www.philosophypages.com/dy/a.htm#abs In order to make sure that we use the right rules, you'd have to say what the rules of your system are.

You don't have permission to post.