I.   Use the method described in lesson 10b for each of the
            following derivations:

           A.   Derive P <-> Q from

               1.   P                       Premise
               2.   Q                       Premise
               3.       P                   Assumption
               4.       Q                   3, R
               5.   P -> Q                  3-4, CP
               6.       Q                   Assumption
               7.       P                   1, R
               8.   Q -> P                  6-7, CP
               9.   (P -> Q) & (Q -> P)     5, 8, Conj.
              10.   P <-> Q                 9, Equiv.

           B.   Derive P <-> (P v Q) from

               1.   ~Q                      Premise
               2.       P                   Assumption
               3.       P v Q               2, Add.
               4.   P -> (P v Q)            2-3, CP
               5.       P v Q               Assumption
               6.       P                   1, 5, DS
               7.   (P v Q) -> P            5-6, CP
               8.   (P -> (P v Q)) & ((P v Q) -> P)
                                            4, 7, Conj.
               9.   P <-> (P v Q)           8, Equiv.

           C.   Derive P <-> (P & Q) from

               1.   Q                       Premise
               2.       P                   Assumption
               3.       P & Q               1, 2, Conj.
               4.   P -> (P & Q)            2-3, CP
               5.       P & Q               Assumption
               6.       P                   5, Simp.
               7.   (P & Q) -> P            5-6, CP
               8.   (P -> (P & Q)) & ((P & Q) -> P)
                                            4, 7, Conj.
               9.   P <-> (P & Q)           8, Equiv.

      II.   Without using CP, write another derivation for the problem in
            I.A.

           A.   Derive P <-> Q from

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