\section*{6. For APPLICANTS IN $\left\{ \begin{array} { l } \text { COMPUTER SCIENCE } \\ \text { MATHEMATICS \& COMPUTER SCIENCE } \end{array} \right\}$ ONLY.}
(i) Alice, Bob, Charlie and Dianne each make the following statements:

Alice: I am telling the truth.\\
Bob: Alice is telling the truth.\\
Charlie: Bob is telling the truth.\\
Dianne: Charlie is lying.

Only one of the 4 people is telling the truth. Which one? Explain your answer.\\
(ii)They now make the following statements:

Alice: Bob is lying.\\
Bob: Charlie is lying.\\
Charlie: I like beer.\\
Dianne: $2 + 2 = 4$.

Now two of the four people are telling the truth. Which two? Explain your answer.\\
(iii) They are now joined by Egbert. They each make the following statements:

Alice: I like wine.\\
Bob: Charlie is lying.\\
Charlie: Alice is lying.\\
Dianne: Alice likes beer.\\
Egbert: Alice likes beer.

Now three of the five people are telling the truth. Which ones? Explain your answer.\\