# Becoming proficient in Symbolic Logic

1. Jan 30, 2012

### bodhi dharma

1. The problem statement, all variables and given/known data

I'm not sure where this goes, but I'll post it here, as it seems to be a quasi-mathematical subject.

Anyway, I was doing derivations from conclusions using implication rules, and I was quite confused to say the least.

The rules of implication are: Modus Ponens: A->B, ~B/~A Hypothetical syllogism: A->B, B->C/A->C Modus Tollens: A->B, ~B/~A Disjunctive syllogism: AvB, ~A/B AvB, ~B/A Simplification: A&B/A A&B/B Addition: A/AvB B/AvB Conjunction: A, B/A&B Constructive dilemma: (A->B)&(C->D), AvC/BvD

Now, when I applied these to some problems, I had numerous difficulties. I'm not sure where to begin. Can someone help me out?

2. Relevant equations

Here were some of the questions:

derive S&N from:

1. (V<->N)&S

2. (GvS)->(V&N)

3.

4.

derive ~Z from:

1. G

2. (G&D)->~Z

3. G->~(Zv~M)

4. (Zv~M)vD

5.

6.

derive A from:

1. R->T

2. RvA

3. F

4. F->(~T&K)

5.

Now my purpose in posting these sample problems is to figure out how to do this stuff, as my skill at symbolic logic is weak enough as it already is. Here's a few more:

derive SvE:

1. (D<->Z)->E

2. Z&D

3. Z->(Xv(D<->Z))

4. X->S

5.

derive GvN:

1. ~U

2. CvB

3. (HvB)->(I&G)

4. C->U

5.

derive K:

1. (XvP)&R

2. P->Q

3. X->Z

4. (ZvQ)->(K&J)

5.

derive ZvU:

1. WvA

2. V&G

3. ~N->Z

4. W->~N

5. (VvH)->(A->U)

6.

derive I:

1. Tv~P

2. ~T&(Q->H)

3. (A->T)&(X->I)

4. (~T&~P)->(AvX)

5.

I hope I'm not boring anybody by posting this, but it's because I'm pretty lost right now and I really want to master symbolic logic and need all the help and advice I can get.

Also, is there any software that can be used to generate proofs? I've heard of logic proof generators, but I'm not sureas to where to find these.

Are there any good books on mastering symbolic logic?

I'd also like to talk to people who have expertise in this subject area as well.

3. The attempt at a solution

Here's one attempted solution. The derivation of A:

Pr.1. R->T

Pr.2. RvA

Pr.3. F

Pr.4. F->(~T&K)

Pr.5. ~T&K 3,4 Modens Ponens

Pr.6. ~T 5 Simplification

Pr.7. ~R 1,6 Modens Tollens

Concl.8. A 2,7 Disjunctive syllogism

2. Jan 30, 2012

### bodhi dharma

I'll post more when I get back later on today.

3. Jan 31, 2012

### e^(i Pi)+1=0

I just wanted to say that you have excellent taste in user names.