# Logic: Proofs

1. Jan 3, 2012

### particlepat

Hey everyone I'm new to the forums and I came here because I completely stumped. This is basic logic but for some reason I'm having trouble with this one.

1. The problem statement, all variables and given/known data
1) ~(A * G)
2) ~(A * E)
3) G v E / prove ~(A * F)

As I go through and show each step I have to give which rule is being applied.

2. Relevant equations
Rules I can use
Modus Ponens MP
Modus Tollens MT
Disjuctive Syllogism DS
Simplification Simp
Hypothetical Syllogism HS
Constructive Dilemma CD
Conjunction Conj
DeMorgan DM
Associativity Assoc
and Distribution Dist

Rules I cant use
Transposition
Implication
Exportation
Tautology

3. The attempt at a solution
The first time I proved it but after reading the instructions I realized I'm not supposed to use tautology or material implications. It may be as simple as not knowing exactly how to simplify something like ~(A * G) when it's when the whole equation is negated.

Any help would be great.

2. Jan 3, 2012

### Dick

I'm not really an expert on all of this logic terminology, but isn't simplifying ~(A * G) DeMorgan?

3. Jan 3, 2012

### particlepat

right so assuming I did the following:

1) ~(A * G)
2) ~(A * E)
3) G v E /need to prove ~(A * F)
4) ~A v ~G because DM on line 1
5) ~A v ~E because DM on line 2

This is about where I get stuck...

4. Jan 3, 2012

### Dick

Like I said, I don't know logic formalism very well. But it's pretty clear you want to prove A is false. Can you do that using one of those rules?