Three people decide to go out for burgers. They are either Knights, which always tell the truth, Knaves, which tell truths and lies in an alternating pattern, or Liars, which always tell lies.
They each want a burger, and want to get 4 toppings from the list of 7 (ketchup, mustard, onions, relish, tomato, cheese, lettuce) and give their order as follows:
A: I want ketchup, mustard, onions, lettuce, relish.
B: A wants tomato too, and he doesn't want mustard. I want ketchup, tomato, cheese, lettuce.
C: B doesn't want ketchup, and he doesn't want mustard. A doesn't want relish. I want mustard, tomato, cheese, lettuce.
After giving the orders to the burger cooker, he figures out what they want.(as anyone who can cook well must be really intelligent)
If all three people didn't all want a certain topping, what do the three people actually want as their four toppings on their burger?
(Note: I placed commas and periods to remind that each item/statement separated by commas is a separate statement.)