How do i Prove the following through natural deduction

Question

Using conjunction elimination/introduction; disjunction elimination/introduction; contidional elimination/introduction, negation elimination/introduction; biconditional elimination/introduction.

1.
A -->(B-->C)
____________
(A-->(D&(E&B)))-->(A-->C)



2.
A-->B
~A-->~C
_________
C-->B

3.
C v ~C
C --> ~B
~C --> ~N
___________
~B v ~N


4.
F-->(GvH)
G
_________
F-->H

Answer 1

Please post individual questions separately, to get the best chance of getting them answered.  

 

I'm reviewing to see if I can find the proper form of response for your class.   I'm not up on "natural deduction" as a sub-species of logic - I'm falling back on formal logic and talking my way through it. 

 

If you can post a proof of any other problem so I can see how your professor wants it, symbolically, then I can rephrase my answers in a way that will help you the most.  

 

Here, I'm going to use English so you can at least see how I'm thinking it through.

 

 

Let's look at item 4.

 

PROBLEM 4

 

The first equation translates to English this way :

 

If False is true it implies that (G OR H) must be true

 

G is True

 

Given the above, can you prove that F being true implies H is true?

 

(Initially I wrote a bunch of stuff here, but it's all irrelevant.  If False is true, you can prove anything through a principle called ex falso quodlibet)

 

Assume F

H

Therefore F -> H