Group I Rules (Deductive Argument Help)

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Reply Wed 15 Apr, 2009 11:29 am
Hi! I am new to propositional & deductive arguments.Our homework is covering all of these arguments. I somewhat understand some of these concepts (ie., MP & MT), but our homework is much more complex (3+ steps instead of just 2) & I'm uber confused. I was wondering if you could give some of your amazing explanations again. I need every minute detail, no matter how obvious it may seem! Any who, here are a few problems from my homework:

Instructions: "Construct deductions for each of the following, using the Group I rules. Each can be done in just a step or two."

here is what they mean by Group I rules:

Group I
1. Modus ponens (MP)
2. Modus tollens (MT)
3. Chain Argument (CA)
4. Disjunctive Argument (DA)
5. Simplification (SIM)
6. Conjunction (CONJ)
7. Addition (ADD)
8. Constructive Dilemma (CD)
9. Destructive dilemma (DD)


Problem #6)
1. ~P
2. ~(P & S) v Q
3. ~P --> ~Q /therefore, ~(R & S)


Problem #8)
1. P --> ~(Q & T)
2. S --> (Q & T)
3. P /therefore, ~S

Problem #9)
1. ( P v T) --> S
2. R --> P
3. R v Q
4. Q --> T /therefore, S

I have a test on Tuesday & this material is a complete blank to me!!! thanks so much!
 
VideCorSpoon
 
Reply Thu 16 Apr, 2009 11:33 am
@ValidandNotinUse,
Hey Valid!

Alright. I have 8 and 9 down with 2 steps. I'm not quite sure if you are required to do 3 steps, but I found solutions in 2. Problem number 6 is an issue in that I had to use a replacement rule to execute the proof, and it was a few more steps than what you are allowed to use. I'll try to hash it out, but I'll go over problem 8 and 9 and how to attack them.

So here is your first problem, complete with step-by step inferences to reach the conclusion with the strategy for attacking proof in general incorporated into it..

http://i44.tinypic.com/1zfh40h.jpghttp://i43.tinypic.com/2mea0bt.jpg


Let's approach this from the perspective of the 4 step process.

Step 1 - Look for the single variable. We do not have it.

Step 2 - Look for a conditional or a disjunction which are most likely to help us start off.
We DO have that. We have two conditionals, but we also have a disjunction. It is usually the case that a proof is constructed by the teacher to set up a constructive dilemma. It is evident in this proof. A constructive dilemma needs two conditionals, a disjunction, and they need to fit the form where the antecedents of both conditionals match both disjuncts of the disjunction. We have this in lines 2, 3, and 4 and we can derive P v T. Go to step 3.
Step 3 - Look for every derivation possible
 
ValidandNotinUse
 
Reply Sun 19 Apr, 2009 07:52 pm
@ValidandNotinUse,
thread has been moved to:

http://www.philosophyforum.com/forum/philosophy-forums/branches-philosophy/logic/1514-propositional-logic-symposia-6-complex-partial-truth-tables-2.html
 
M Margolis1987
 
Reply Fri 8 May, 2009 10:48 am
@ValidandNotinUse,
I need help, I have a final exam on Monday and the main problem I have is understanding how to create the steps for deductive arguments. I've tried to look at it but have a hard time seeing how this works. I really need any help possible, plus I'm very weak in math, so I have a lot of trouble with problem solving.

Here's some practice problems I'm trying to do to study for that section of the exam.
I.

1. P->R
2. R->Q /:. ~P v Q

II.
1. ~P v S
2. ~T -> ~S /:. P -> T

III.

1. F -> R
2. L -> S
3. ~C
4. (R & S) -> C /:. ~F v ~ L

I'm trying to understand how to actually derive the conclusions from the premises, but I need a lot of help with getting the steps down. I tried looking for variables but that's confusing me more. Someone please help me. I'm in desperate need of some helpful advice.
 
ValidandNotinUse
 
Reply Fri 8 May, 2009 12:20 pm
@ValidandNotinUse,
One thing that was really helpful for me was to write out the problem and the suspected Argument type right beside it (i.e., if I suspected it was MT or MP or ADD, etc).

It helped me to see the Group I type right next to the problem I was working on. Then you can better see the relationship of the variables.
 
 

 
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