I.   In the following derivations, indicate the line(s) that each
            line is derived from, and the rule by which each line is
            derived.

           A.   Derive P from

               1.   ~P -> Q                 Premise
               2.   ~Q v ~Q                 Premise
               3.   ~(Q & Q)
               4.   ~Q
               5.   ~~P
               6.   P

           B.   Derive (P & Q) v (P & Q) from

               1.   R & Q                   Premise
               2.   S & (P & T)             Premise
               3.   Q & R
               4.   Q
               5.   (S & P) & T
               6.   (P & S) & T
               7.   P & (S & T)
               8.   P
               9.   P & Q
              10.   (P & Q) v (P & Q)

           C.   Derive (P & Q) v (P & Q) from

               1.   R & Q                   Premise
               2.   S & (P & T)             Premise
               3.   S & (T & P)
               4.   (S & T) & P
               5.   P & (S & T)
               6.   P
               7.   P & (R & Q)
               8.   P & (Q & R)
               9.   (P & Q) & R
              10.   P & Q
              11.   P & (Q v Q)
              12.   (P & Q) v (P & Q)       11,

           D.   Derive P <-> Q from

               1.   ~P v Q                  Premise
               2.   ~P -> ~Q                Premise
               3.   P -> Q
               4.   Q -> P
               5.   (P -> Q) & (Q -> P)
               6.   P <-> Q

           E.   Derive (P & Q) -> R from

               1.   P -> R                  Premise
               2.   (P -> R) v ~Q
               3.   ~Q v (P -> R)
               4.   Q -> (P -> R)
               5.   (Q & P) -> R
               6.   (P & Q) -> R