You are traveling in a certain country where every inhabitant is either a trutht

Question

You are traveling in a certain country where every inhabitant is either a truthteller who always tells the truth or a liar who always lies. You meet two of the inhabitants of this country, you meet Rothwold and Grymlin. Rothwold says, "Either I am a liar or Grymlin is a truthteller." Is Rothwold a liar or a truthteller? What about Grymlin? Explain your answer. Traveling on, Percival and Llewellyn. Percival says, "At least one of us is a liar." Is Percival a liar or a truthteller? What about Llewellyn? Explain your answer. Finally, you meet Merlin and Meredith. Merlin says, "If I am a truthteller, then Meredith is a truthteller." Is Merlin a liar or a truthteller? What about Meredith? Explain your answer.

Explanation / Answer

1. The answer is both are telling the truth.

The Statement is "If I am a truthteller then Meredith is a truthteller". It cannot be a lie. It turns out to be IMPOSSIBLE. If it were a lie, Merlin would have to be a liar. "If I (Merlin) am a truthteller Then Meredith is a truthteller" is TRUE, if the antecedent is FALSE! I (Merlin) am a truthteller is a FALSE statement, if Merlin is a LIAR. If FALSE (P) Then consequent (Q) is ALWAYS TRUE. No way could be a liar make that statement.

P Q | if P then Q             P       ------> Q

----------------- antecedent consequent

T T |      T                  P       implies Q

T F |      F

F T |      T     <--- antecedent P is FALSE, if P then Q is TRUE

F F |      T     <--- antecedent P is FALSE, P implies Q is TRUE

"If I am a truthteller, then Meredith is a truthteller" must be a TRUE statement, since having it be a FALSE statement turned out to be impossible.This means that Merlin is a truthteller, this means that he very expressively said what was TRUE. Since I am a truthteller is then a TRUE antecedent, with the pronoun I be a self-reference to Merlin, the consequent Q has to be true, i.e.Meredith HAS TO BE a truthteller.

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