I think if you draw out the logical statements I've made one implication correctly. I claimed A implies B is a true statement and that if A implies B is true, that doesn't mean B implies A or ~A implies ~B. (although ~B does imply ~A if A implies B).

True:

  A implies B: Printed money implies a rise of corruption
  ~B implies ~A: Low corruption implies money wasn't printed

False:

  B implies A: A rise in corruption implies printed money
  ~A implies B: Not printing money implies low corruption

I did not say A and B are independent, I said A implies B, not A IFF B.