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Homework Help: Logic: Proofs

  1. Jan 3, 2012 #1
    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
    Addition Add
    DeMorgan DM
    Associativity Assoc
    and Distribution Dist

    Rules I cant use

    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. jcsd
  3. Jan 3, 2012 #2


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    Science Advisor
    Homework Helper

    I'm not really an expert on all of this logic terminology, but isn't simplifying ~(A * G) DeMorgan?
  4. Jan 3, 2012 #3
    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...
  5. Jan 3, 2012 #4


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    Science Advisor
    Homework Helper

    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?
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