Chapter 1.2, Problem 40E

Exercises 36-42 are puzzles that can be solved by translating statements into logical expressions and reasoning from these expressions using truth tables.

40. Four friends have been identified as suspects for an unauthorized 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, who did it? Explain your reasoning.

b) If the authorities also know that exactly one is lying, who did it? Explain your reasoning.