Solving a Logic Problem: Prove ~(A * F)

[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.

Homework Statement

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.

Homework Equations

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

Rules I can't use
Transposition
Implication
Exportation
Tautology

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.

 

[Dick]

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

 

[particlepat]

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

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...

 

[Dick]

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...

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?