Campus Security received a report that a student in the Robert Surtees Centre was walking around without a face mask. When security arrived at the library to investigate, they met three students named, P, Q and R. When questioned by security, the students gave the following statements. a) P: If R did not do it, then Q was the one who walked around without a mask.

b) Q: Both P and R walked without a mask or P was the only one without a mask.

c) R: We all walked without our masks in the building.

The security knew that only one student broke the face mask rule. To figure out the guilty student, they sought help from a group of Math 1056 students in the library who were working on their final exam, and they asked the following question to the group. They had two questions.

Given the statements above ,

i) If all students are lying, who is guilty?

ii) If exactly one of the students lying, who is guilty?

Using rules of inference and other discrete mathematics theorems, facts and definitions