prepositional logic

40. Four friends have been identified as suspects for an unau- thorized access into a computer system. They have made statements to the investigating authorities. Alice said, "Carlos did it." John said, "I did not do it. Carlos said, "Diana did it. Diana said, Carlos lied when he said that I did it." a) If the authorities also know that exactly one of the four suspects is telling the truth, who did it? Explain your reasoning. b) If the authorities also know that exactly one is lying, who did it? Explain your reasoning