Hey, can someone help me in this problem? Thanks Suppose we would like to prove

Question

Hey,

can someone help me in this problem?

Thanks

Suppose we would like to prove an implication p => q in the context of the given assumptions. We are free to assume p as an axiom even though it might not be a given assumption - but only during the proof of q. Moreover, the section of the proof from the line containing p to the line containing q is indented, and the line immediately following that indented section is the implication p=> q. The following example illustrates conditional proof. Homework: Completely justify the proof above (indicate to which items in the proof above the tautologies are applied).

Explanation / Answer

1) r

2)!r or p or q

     from second given tautology statement we can state !r , p ,q are true and from first statement we can state r is true and can do following assumption.

3) p

   this can be derived as true

4) from second we can assume that

        !p or q is tautology

from 3 and 4 we can derive

5) q as tautology

and hence p and q are tautology, we can derive

6) p if then q as tautology

    

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