that's where knowledge of the "If and ONLY IF A then B" is
   important. To me, that helps lead the mind into more vague
   examples, such as "IF A then B". The "If and only if" sets one
   side in concrete. There is a "MUST", an "ABSOLUTE". I think part
   of the misunderstanding people have with "If A then B" is the
   "sometimes-ness" factor, or mistaking an IF with an IF AND ONLY
   IF. Please correct me if I am mistaken in any of this. This is
   just "top of the head".