Logic Proof Help

[VideCorSpoon]

Originally posted by SteveP;

Hello everyone, this is my first post here. I'm glad to find some place where I can talk with people interested in Philosophy too. I'm mainly interested in Logic though.

I did have a question though, I'm taking basic philosophy right now and our professor gave us some questions to go over. I am completely stumped on four of them. He gave us a sheet with 18 rules for inference and replacement.

we are supposed to prove the arguments as valid. I'm hoping someone can help explain this to me.
And Logic pro's in the room? Don't laugh, they're hard for me.

Anyhow, here are the problems I have

1:
[A ꜆ (B v C)] ꜆ (D ꜆ A)
~A
/∴ ~D


2:
A ꜆ B
/∴ A ꜆ ~(~B . ~C)

3:
~N ꜆ S
S ꜆ ~A
~A ꜆ ~V
/∴ V ꜆ (A . N)

4:
~W ꜆ ~F
~F ꜆ ~(E v A)
~E ꜆ S
P ꜆ A
/∴ ~W ꜆ (S . ~P)


Thanks in advance for any help you can give me!

[SteveP]

Ok, here's the image for the problem because the symbols above are messed up.


or the link to the image page if the first doesn't work bayimg - image: Picture 1.png - free uncensored image hosting

[VideCorSpoon]

First question... Is the weather to your liking?

Second... Can you solve this with additional lines or are these lines the only lines you can use?

Thirdly, at what point in the class are you? Midterm?

Fourthly, what book are you using? Pray to Geebus if you are using the Bergmann et al edition of "The Logic Book."

Fifthly, What topic did you last cover?

Sixthly, Do you think ponies are pretty? You will be judged on your response quite thoroughly.

[SteveP]

The weather is exemplary, thank you for asking.

I'm not sure exactly what you mean by solving with additional lines... but we can create lines using the rules of inference and replacement.

Actually this is near the end of the class. These are some example questions for the final on monday!!!!

"A concise introduction to Logic"

Chapter 7, Natural Deduction in propositional logic - or... these 18 rules we have.

I think Ponies are gangly and ugly. Shetland ponies are, however, still unattractive despite their lack of gangliness.

[VideCorSpoon]

We are pleased by your response and shall make a sacrificial offering of a shetland pony to the Gods of Jelly to give you good luck for your exam on Monday. LOL!

Give me a little time and I'll solve them in the easiest way possible and post them and then we'll look over them if you have any other questions.

[SteveP]

That sounds excellent. If you would include what lines you used on what rules (i.e. [1,3 MP] - lines one and three, rule modes ponens) that would really help me understand how you figured it out.

[VideCorSpoon]

On problems 2, 3, and 4 the answers have a period in between the variables i.e. A --> ~ (~B . ~C)

Is this a conjunction symbol in your book?

[VideCorSpoon]

First… I sympathize with you. Your teacher is for lack of a better word an Icelandic variety of Dill… well, you get the picture. There are so many ingrained variability’s in these problems that it takes a major short cut like a conditional or indirect proof just to fit it on the page. This guy has gone all out. I shall sacrifice two ponies.

I have just solved and simplified the fourth problem for you. The hardest is the easiest. But it requires a conditional proof if your comfortable with it… otherwise the proof is 28 lines long with the basic inference and replacement rules.


The other problems will take a while... or not at all. Like I said, this guy is really something for a beginning propositional logic class.

[SteveP]

Yeah, she said that Conditional Proofs are Ok. and also IP's

I'm gonna try and figure out what you did there.

[SteveP]

I assume that the --> you wrote is the horseshoe symbol I used?