I.   Derive the following tautologies:

           A.   P v ~P

           B.   ~(P & ~P)

           C.   P <-> (~P -> P) (Note: pay attention to this one. It will
                form the basis for the next lesson.)

      II.   Without using Repetition (R), derive P -> P.

     III.   Without using Material Implication (Impl.), derive (~P v Q) ->
            (P -> Q). (Hint: Use one conditional proof inside another.)

      IV.   Without using Exportation (Exp.), derive [(P & Q) -> R] -> [P
            -> (Q -> R)].

       V.   Without using Hypothetical Syllogism (HS), derive [(P -> Q) &
            (Q -> R)] -> (P -> R).