I.   Use IP in derivations for the following problems:

           B.   Derive P v ~P from scratch

           A.   Derive P -> P from scratch

           C.   Consider the following proof:

               1.   P & ~Q                      Premise
               2.   ~~P & ~Q                    1, DN
               3.   ~(~P v Q)                   2, DM
               4.   ~(P -> Q)                   3, Impl.

                Derive ~(P -> Q) from (P & ~Q) without using any rule that
                the preceding proof used.

           D.   Without using De Morgan's Theorems (DM), derive ~(P v Q)
                from

               1.   ~P                          Premise
               2.   ~Q                          Premise

           E.   Without using De Morgan's Theorems (DM), derive (~P v ~Q)
                -> ~(P & Q) from scratch. (Hint: use an in indirect proof
                inside of a conditional proof.)