Three students X, Y and Z are accused of cheating in assignment. During the interrogation they make the following claims:

• X says: Y cheated and Z did not.
• Y says: If X cheated then Z cheated too.
• Z says: I did not cheat. One of the others, or maybe both of them cheated.

(a) Represent above statements as wffs in propositional logic.

(b) Are the three statements contradicting each other or they are satisfiable?

(c) Assuming that nobody lied, who is innocent and who cheated?