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Four logicians (A, B, C, and D) have fixed identities: two always tell the truth, and two always lie. You ask A: "Is B a liar?" A whispers. You ask B: "What did A just say?" B replies: "A said that C is a liar." D immediately says: "Do not believe him, B is lying!" Based strictly on this information, which statement can be deduced with absolute certainty?
  1. B and D have opposite identities
  2. A is a truth-teller
  3. D is a truth-teller
  4. None of these
Explanation

D's statement directly concerns whether B is lying.

If D tells the truth, B lies; if D lies, B tells the truth.

Therefore, B and D must have opposite identities.


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