6. For APPLICANTS IN $\left\{ \begin{array} { l } \text { COMPUTER SCIENCE } \\ \text { MATHEMATICS \& COMPUTER SCIENCE } \end{array} \right\}$ ONLY.
(i) Alice, Bob, and Charlie make the following statements: Alice: Bob is lying. Bob: Charlie is lying. Charlie: $1 + 1 = 2$. Who is telling the truth? Who is lying?. Explain your answer. (ii) Now Alice, Bob, and Charlie make the following statements: Alice: Bob is telling the truth. Bob: Alice is telling the truth. Charlie: Alice is lying. What are the possible numbers of people telling the truth? Explain your answer. (iii) They now make the following statements: Alice: Bob and Charlie are both lying. Bob: Alice is telling the truth or Charlie is lying (or both). Charlie: Alice and Bob are both telling the truth. Who is telling the truth and who is lying on this occasion? Explain your answer.
(i) [3 marks] Clearly Charlie is telling the truth. Consequently Bob is lying which makes Alice's statement true. [0pt]
\section*{6. For APPLICANTS IN $\left\{ \begin{array} { l } \text { COMPUTER SCIENCE } \\ \text { MATHEMATICS \& COMPUTER SCIENCE } \end{array} \right\}$ ONLY.}
(i) Alice, Bob, and Charlie make the following statements:
Alice: Bob is lying.\\
Bob: Charlie is lying.\\
Charlie: $1 + 1 = 2$.\\
Who is telling the truth? Who is lying?. Explain your answer.\\
(ii) Now Alice, Bob, and Charlie make the following statements:
Alice: Bob is telling the truth.\\
Bob: Alice is telling the truth.\\
Charlie: Alice is lying.\\
What are the possible numbers of people telling the truth? Explain your answer.\\
(iii) They now make the following statements:
Alice: Bob and Charlie are both lying.\\
Bob: Alice is telling the truth or Charlie is lying (or both).\\
Charlie: Alice and Bob are both telling the truth.\\
Who is telling the truth and who is lying on this occasion? Explain your answer.