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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 meet three of them -- Yulia, Brendan, and Christine -- in the hallway one day and decide that you want to determine each of their roles, Truther or Liar.
- You ask Yulia: "What is your role in Logic Club?"
- She answers in Russian, so you cannot understand!
- You turn to Brendan and ask: "What did Yulia say?"
Brendan replies: "Oh, she just said that she is a Liar."
- Yulia chimes in (in English) to say: "That's correct."
- But Christine jumps in to say: "Wait, don't believe them; they're both Liars!"
What are the roles of Yulia, Brendan, and Christine?
Which are Truthers and which are Liars?