Group I Rules (Deductive Argument Help)

1. Philosophy Forum
2. » Logic
3. » Group I Rules (Deductive Argument Help)

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)
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

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..

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

Sun 19 Apr, 2009 07:52 pm
@ValidandNotinUse,

http://www.philosophyforum.com/forum/philosophy-forums/branches-philosophy/logic/1514-propositional-logic-symposia-6-complex-partial-truth-tables-2.html

M Margolis1987

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

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.

1. Philosophy Forum
2. » Logic
3. » Group I Rules (Deductive Argument Help)