Figuring out Natural Deduction problem but can't find mistake

[krob]

I'm in undergrad and I unexpectedly began taking a discrete math class, everything was sunshine and rainbows until this chapter.... All in all, Below is the Natural deduction problem with its premise and intended conclusion and these are my steps. I can't see where I'm going wrong, any ideas? Thanks :)

(¬A ∨ (¬B ∨ ¬C)) ⊢ (((¬B ∨ ¬C) → (D ∧ ¬D)) → ¬A)
(~A\/(~B\/~C)):PR
    A:AS
        (~B\/~C)->(D/\~D):AS
            ~(~B\/~C):AS
                (~B\/~C):AS
                !?:~E4,5
                D/\~D:X6
            (~B\/~C)->(D/\~D):->I5-7
                (~B\/~C):AS
                D/\~D:->E8,9
                D:/\E10
                ~D:/\E10
                !?:~E11,12
                ~A:X13
(((¬B ∨ ¬C) → (D ∧ ¬D)) → ¬A):IP2-13

 

[Mark44]

I'm in undergrad and I unexpectedly began taking a discrete math class, everything was sunshine and rainbows until this chapter.... All in all, Below is the Natural deduction problem with its premise and intended conclusion and these are my steps. I can't see where I'm going wrong, any ideas? Thanks :)

(¬A ∨ (¬B ∨ ¬C)) ⊢ (((¬B ∨ ¬C) → (D ∧ ¬D)) → ¬A)
(~A\/(~B\/~C)):PR
    A:AS
        (~B\/~C)->(D/\~D):AS
            ~(~B\/~C):AS
                (~B\/~C):AS
                !?:~E4,5
                D/\~D:X6
            (~B\/~C)->(D/\~D):->I5-7
                (~B\/~C):AS
                D/\~D:->E8,9
                D:/\E10
                ~D:/\E10
                !?:~E11,12
                ~A:X13
(((¬B ∨ ¬C) → (D ∧ ¬D)) → ¬A):IP2-13

I'm having a hard time with the symbols here -- I'm more used to the symbols used in mathematical logic.
What is this symbol ⊢ ? Same as or different from → ? And elsewhere you have :->

What is the given premise here? And what is it that you are supposed to prove?

There are a lot of abbreviations that I don't get, among them are:
PR
A:AS
AS
E4,5
X6
I5-7
E8,9
X13
IP2-13

The first line you write is (¬A ∨ (¬B ∨ ¬C)) ⊢ (((¬B ∨ ¬C) → (D ∧ ¬D)) → ¬A)
Clearly D ∧ ¬D is false (or the empty set if we're dealing with sets).

If you want help, you need to provide a lot more explanation of what you're doing.

 

[krob]

I'm having a hard time with the symbols here -- I'm more used to the symbols used in mathematical logic.
What is this symbol ⊢ ? Same as or different from → ? And elsewhere you have :->

What is the given premise here? And what is it that you are supposed to prove?

There are a lot of abbreviations that I don't get, among them are:
PR
A:AS
AS
E4,5
X6
I5-7
E8,9
X13
IP2-13

The first line you write is (¬A ∨ (¬B ∨ ¬C)) ⊢ (((¬B ∨ ¬C) → (D ∧ ¬D)) → ¬A)
Clearly D ∧ ¬D is false (or the empty set if we're dealing with sets).

If you want help, you need to provide a lot more explanation of what you're doing.

Hi Mark.

Thanks for responding, and also you're right I should have been clearer. So the first and only premise here is (~A\/(~B\/~C)). ⊢ is the symbol that concludes that whatever follows is the conclusion of the argument before it, hence (¬A ∨ (¬B ∨ ¬C)) ⊢ (((¬B ∨ ¬C) → (D ∧ ¬D)) → ¬A). PR is the premise, AS is an assumption, E is elimination, X is explosion, I is introduction, and IP is indirect proof. It is a weird syntax, I utilize it mainly because it is what I use in my classes. Also since we know that (D/\~D) is false as it is a contradiction or in simple words a premise leads to a conclusion that doesn't make sense, we have to use the theorem of explosion along with other natural deduction theorems to get to the conclusion from the premise.

I do hope this clears up what I meant, I am sorry for the confusion and can clarify more if necessary.

 

[Mark44]

hence (¬A ∨ (¬B ∨ ¬C)) ⊢ (((¬B ∨ ¬C) → (D ∧ ¬D)) → ¬A)

What's the difference between ⊢ and → ?
Do they both mean "implies"?

Why is this expression, (D ∧ ¬D), in the line I quoted? It's obviously false. Tossing in D ∧ ¬D for false needlessly complicates things, IMO, since there is no mention of D in the premise.
From what I can tell, your goal is to show that (¬A ∨ (¬B ∨ ¬C)) implies ¬A
For the expression (¬B ∨ ¬C), there are two possibilities: it's either false or it's true. Since neither B nor C shows up in the desired conclusion, I don't see why you can't just replace (¬B ∨ ¬C) with something else, say D.

For the two cases for (¬B ∨ ¬C), what does the premise simplify to if you assume that (¬B ∨ ¬C) is true?
What does the premise simplify to if you assume that (¬B ∨ ¬C) is false?

Your proof would be much easier to follow if 1) you explained in words what you are doing, and 2) eliminated unnecessary complications such as (D ∧ ¬D).