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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.
Members of Illogical Club sometimes tell lies and sometimes tell truths. It depends on their mood! (However, members of Illogical Club do happen to know which members of Logic Club are Truthers and which are Liars; they may just choose to tell lies or truths about their knowledge.)
(In this first encounter with Illogical Club, you know who belongs to which club. In the future, you may have to determine which club someone belongs to, based on their statements!)
You attend a campus-wide recruitment fair. There, you find a table for Logic Club attended to by two members thereof: Larry and Linda.
Next to them is a table for Illogical Club, attended to by a sole member thereof: Igor.
You approach the two tables and, unprovoked, the club members speak to you:
- Igor says: "Larry is a Truther."
- Larry says: "If what Igor just said is a truth, then Linda is a Liar."
- Linda says: "What Igor just said is a lie."
What are the roles of these Logic Club members, and why? Is Igor's statement a truth or a lie?
Note: A correct answer is good, but an explanation is better.