has anyone started assignment 2, some question 2 ( Formal proofs) problems, please help if you can?

Are we allowed to change a premise to its equivalent before starting the proof or are we supposed to do it in the proof? ie

~(Q & R) can be stated rather as ~ (Q V ~R) (De morgans)

Can we change the premise to this???

Thanks!

.

I'm also having some headaches about this module and decided to wait until after the 19th of May when there will be discussion classes in Pretoria on formal proofs. I'm not sure if there will be any discussion classes in other regions, see TL103.....

I wish there were more examples or exercise solutions, as it doesn't help getting stuck alone at home on an exercise and not being able to get past it...

Has anyone done Q1 yet?

Yes, I completed Q1, actually the easiest part of the assignment, what helps is to look at the translation table in the text-book (chapter 7). I'm not sure exactly where, but look at the index at the back under translation, you will find reference to every natural language phrase applicable (such as "unless", "but", "if and only if" etc.) and how to interpret in FOL. Be careful with some of the interpretations as it is easy to do it the wrong way round. Look at the link below, you'll find interesting hits, tips and FAQs.......

http://www-csli.stanford.edu/LPL/Students

gosh i got q2 and q3 but not q1 ... ok so are you saying for Q1 you used an equivalent? ie did you change the original premise to something easier to work with? (Don't have textbook with me)

I've completed and submitted my assignment.
Iva, I did make use of DeMorgan, but not as a premise, as a further part of the proof.
Use the link supplied by FerdieL, it is VERY helpful.
Reanie

Thanks both of you! this link looks just what i need!!

i have done sort of half of 2.4 as well using that deMorgans law... might ask more questions again soon, just want to finish 2.1 first....

wait..Reanie you used de Morgan within the proof ? what rules do you use when you know something is a law? this was my confusion. i proved that question ( 2.3) but changed the premise which might cause the proof not to get full marks...

For Q2.3 I've used DeMorgan, getting the one side using a rule and then stating the other side using DeMorgan and again a rule to get my proof. Only have 5 steps for this question.
Of course, I can be totally wrong in my handling.....
Haven't used DeMorgan anywhere else, just elim and intro rules.
Go and look closely at the info in the link that Ferdie gave - you'll find a lot of usefull stuff and examples.

ok i am doing exercise 6.19 from the hints link,

In this exercise the first subproof proves A v C twice and then concludes AvC using v Elim, but with what supporting steps??? i have

1.A v B
2.~B v C
-
| 3. A
|-
| | 4. ~B
| |-
| | 5. A v C v Intro
|
| | 6. C
| |-
| | 7. A v C v Intro
| |
| A v C v Elim <------------- but from what supporting steps ??


This is where i get stuck, i thought this rule should be supported by the 2 subproofs and premise 1 but it doesn't check out on Fitch ???

don't worry sorted...

You are allowed to use both Implication and Equivalence rules, as long as they help you arrive at the desired conclusion.


COS 261 Lecturers

I'm really stuck with 2.3, any hints? I could give an informal proof easily but the rules don't allow me to translate the informal proof into a formal proof.

If you have A V B and you can prove that A is false,how do you then say that B must be true in a formal proof?

The premises are:

R & ~P
P V ~(Q &R)

You have to prove ~Q

I'm also a bit stuck but I think we need to use ~intro and to do that we maybe need to use contradiction? From the first premise it is easy to get R or ~P by using &elim. What I'm not sure about is hout to use Velim to eventually get to Q.

Look at my comment on 2 May to Iva, hope that helps....

Would you mind posting your comment, I'm not too sure which one it is.

Was that link in another post helpful? What chapter do similar examples appear in the book anyway?

Reanie Wrote:
-------------------------------------------------------
> For Q2.3 I've used DeMorgan, getting the one side
> using a rule and then stating the other side using
> DeMorgan and again a rule to get my proof. Only
> have 5 steps for this question.
> Of course, I can be totally wrong in my
> handling.....
> Haven't used DeMorgan anywhere else, just elim and
> intro rules.
> Go and look closely at the info in the link that
> Ferdie gave - you'll find a lot of usefull stuff
> and examples.

FerdieL Wrote:
> Look at the link below,
> you'll find interesting hits, tips and
> FAQs.......
>
> http://www-csli.stanford.edu/LPL/Students

Just remember, I haven't tested my answers with Finch as I did it at work, so my recommendations can be incorrect.

Thanks Reanie

what chapter?

The recommended reading in Tut 101, p 10 is Chapters 5 - 8.
Don't have my book with me, so can't remember where some examples were.

Thanks so much for your help, I'll have a look in the morning.

I probably won't have any work to do so my time is my own until I'm given work to do.

Can you use two assumptions eg:

1. Premise 1: -----
2. Premise 2: -----
3. ----
4. | Assumption 1
5. | Assumption 2
6. -----
7. -----
8. Proved statement

I'd be using two assumptions but not actually proving them, would that be valid?

i'm not sure but i don't think so, u have to prove the assumption first then you can use it ...someone pelase correct me if i'm wrong

Didn't think so, oh well.

Still struggling, any help would be appreciated.

HI tracey, i don't have my stuff at work , but here is some comment,
FIRST as reanie said you can change the 2nd premise using de morgans law ( it helped me do the proof easier (but not necessary) ie:
assumption P V ~(Q &R)
is the same as saying
P V ¬Q V ¬R <--- this is what i changed my 2nd premise to..

from the first premise as its a conjunction, you can use ΛElims to state both R and not P as being true from that. now you have 4 truths to back you up in your proof

after that you must make 3 assumptions :
P,
¬Q,
¬R
and show from each via the rules and supporting steps that ¬Q is true



THe way i approach it is first state what is obvious without needing more proofs , like 1) below
Second :write your assumptions first and determine what you hope to prove from each one:


proof steps:

1) from the first premise you have both ¬P and R stated which u now have available for support/reiteration. now you have 2 premises + 2 truths that you can already use in your proof
2) then you must now show that each of P , ¬Q and ¬R all prove that ¬Q is true..

this is where iwill leave you to play around with it abit

i hope this makes sense and doesn't confuse you. good luck!

Thanks, I'll try to figure it out from what you've told me.

After trying to do a LONG proof, and getting nowhere for this question, what I did realise is that using premise 1...

A ^ -B
Assume C
Then A ^ -B ^ C must be true. Is the step now to try prove a contradiction for this, thus by negation introduction, get -C?

(Know it should be P,Q,R but easier to read like this)

Shaun

Shaun, looks good and maybe if you change the second premise using de Morgan's law you could use that ~Q to get a contradiction.

I might be completely wrong though, I'm giving up on it for now, I'm just not getting it.

I think many of us are a bit lost with this one. The major reason is that the textbook and notes does give some examples but not enough. It rather teaches individual scenarios of specific rules and the problem I have is to find the correct strategy.How does one approach the proofs? What are the golden rules when you look at the goal? How do you know which rules to use when you look at the premises and the conclusion? I have some examples we got from the discussion class on the 19th, but one of those does not verify in Fitch. I'm starting to wonder how many students actually passes the exam the first time round.....