Problem 2:
a. NOT reversible:
   If A = 1, then C = 1 and D = 1, independently of B, which is lost.

b. NOT reversible:
   If C = 1 and D = 0, then we can't know
   if	  A = 1 and B = 0
   or if  A = 0 and B = 1

c. NOT reversible:
   We have no mean of distinguishing A and B, when one is 1 and the other 0.
   cf. b

d. YES:
>> A = [0 0 1 1]

A =

     0     0     1     1

>> B = [0 1 0 1]

B =

     0     1     0     1

>> C = xor(A,B)

C =

     0     1     1     0

>> D = ~A

D =

     1     1     0     0

>> diary off
All output differs. No lost of information.