I.   Solutions to the derivations:

           A.   Derive ~(P & Q) from

               1.   ~P <-> Q                Premise
               2.   (~P -> Q) & (Q -> ~P)   1, Equiv.
               3.   (Q -> ~P) & (~P -> Q)   2, Comm.
               4.   Q -> ~P                 3, Simp.
               5.   ~Q v ~P                 4, Impl.
               6.   ~(Q & P)                5, DM
               7.   ~(P & Q)                6, Comm.

           B.   Derive P v Q from

               1.   P v (P v Q)             Premise
               2.   (P v P) v Q             1, Assoc.
               3.   P v Q                   2, Taut.

           C.   Derive P <-> Q from

               1.   ~(~P v ~Q)              Premise
               2.   ~~P & ~~Q               1, DM
               3.   P & ~~Q                 2, DN
               4.   P & Q                   3, DN
               5.   (P & Q) v (~P & ~Q)     4, Add.
               6.   P <-> Q                 5, Equiv.

           D.   Derive P from

               1.   P <-> Q                 Premise
               2.   Q                       Premise
               3.   (P -> Q) & (Q -> P)     1, Equiv.
               4.   (Q -> P) & (P -> Q)     3, Comm.
               5.   Q -> P                  4, Simp.
               6.   P                       2, 5, MP

           E.   Without using MT, derive ~P from

               1.   P -> Q                  Premise
               2.   ~Q                      Premise
               3.   ~P v Q                  1, Impl.
               4.   Q v ~P                  3, Comm.
               5.   ~P                      2, 4, DS

               or

               1.   P -> Q                  Premise
               2.   ~Q                      Premise
               3.   ~Q -> ~P                1, Trans.
               4.   ~P                      2, 3, MP