Hi everybody, I just want to check to make sure I did this problem right. I know the answer I just need to make sure I did it formally. 1. The problem statement, all variables and given/known data The problem goes like this: a logician is on an island with two groups of people truth-tellers and liars. He meets three individuals, A, B and C. A says something he can't understand, B says "A said he is a liar" and C says "B is telling a lie." Truth-tellers only tell the truth and liars only lie. I was asked to answer this question: Which category do B and C belong? Can you tell anything about the category A fits in? My solution, is this correct? Here ] = negation/not, -> is implication(if/then), and ^ is logical and. Propositions I came up with: A: I am a liar B: A said he is a liar C: B is the liar I thought it out beforehand and C is telling the truth. If A said he is a liar and this is true then he is a truth-teller which means he isn't a liar(a contradiction) and hence B is wrong and therefore C is correct. I formalized it has such: ( (A -> ]A) ^ (B -> (A ^ ]C)) ^ (C -> (]A ^ ]B)) I did a truth table and besides one impossible answer I got C to work out right and nothing else to be true. But is this the right formula afterall? I do not want any answers I just want to know if I'm doing it right. And maybe if your feeling kind you can tell me where to look next if I'm doing it wrong. Again, I know the answer I just need help formalizing it or rather checking my answer. Thanks for all of your time!