The Mom & Pop liquor store employs five cashiers—Adams, Bates, Cox, Drake, and Edwards—each of whom works alone on exactly one day, Monday through Friday.
Adams works only Mondays or Wednesdays.
Bates will not work Wednesdays or Fridays.
Drake and Edwards work on consecutive days.
If Adams and Bates CANNOT work on consecutive days, then which one of the following must be false?