Who is the culprit? " Andy says: "Cindy is guilty". Bart says: "I am not guilty". Cindy says: "Danny is guilty". Danny says: "Cindy lies if she says I am guilty". We know there is exactly one guilty person and exactly one person who says the truth. Who is guilty?" I am getting confused on how to write this symbolically. Is this correct? Then how do I verify who is guilty? $$Andy_{truth} \implies Cindy_{Guilty} \\\ Bart_{truth} \implies \lnot Bart_{Guilty} \\\ Cindy_{truth} \implies Danny_{Guilty} \\\ Danny_{truth} \implies \lnot Cindy_{truth}$$

If any of Andy or Cindy says truth this mean Bart is not guilty which implies Bart also says truth (because if Bart lies then he is not guilty will be a false statement this mean he is guilty which is not our case) , thus we have two persons who says truth, which is not our case.

Therefore ANDY AND CINDY ARE BOTH MAKING FALSE STATEMENTS. THUS CINDY AND DANNY ARE NOT GUILTY.

now if Bart is speaking truth this means Danny is making false statement(because only one person speaks trurth), this mean Cindy was speaking truth which will again a contradiction.

THEREFORE DANNY IS SPEAKING TRUTH AND BART IS GUILTY.