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To join Logic Club, you must decide to always tell the truth or always lie. Members of Logic Club know who among them are Liars and who are Truthers, and they always follow the rules according to their role.
It just so happens that the Math Department faculty are members of Logic Club! You're on your way to find Ben, and you bump into Todd and Patterson standing outside Ben's office.
- You ask them both: "Is Ben in his office now?"
- Todd replies: "Ben is here and Ben is a Liar."
- Patterson replies: "Ben isn't here and Ben is a Liar."
- At that moment, Ben pokes his head out of his office and says: "Hey, I heard you guys! Todd is a Liar!"
- Paterson chimes in again: "Yeah, that's right; Todd is a Liar."
What are the roles of Todd, Patterson, and Ben?
Which are Truthers and which are Liars?