\section*{6. For APPLICANTS IN $\left\{ \begin{array} { l } \text { COMPUTER SCIENCE } \\ \text { MATHEMATICS \& COMPUTER SCIENCE } \end{array} \right\}$ ONLY.}
(i) $\mathrm { A } , \mathrm { B }$ and C are three people. One of them is a liar who always tells lies, another is a saint who always tells the truth, and the third is a switcher who sometimes tells the truth and sometimes lies. They make the following statements:

A: I am the liar.\\
B : A is the liar.\\
C: I am not the liar.\\
Who is the liar among $\mathrm { A } , \mathrm { B }$ and C ? Briefly explain your answer.\\
(ii) P , Q and R are three more people, one a liar, one a saint, and the third a contrarian who tells a lie if he is the first to speak or if the preceding speaker told the truth, but otherwise tells the truth. They make the following statements:\\
$\mathrm { P } : \mathrm { Q }$ is the liar.\\
$\mathrm { Q } : \mathrm { R }$ is the liar.\\
$\mathrm { R } : \mathrm { P }$ is the liar.\\
Who is the liar among P, Q and R? Briefly explain your answer.\\
(iii) $\mathrm { X } , \mathrm { Y }$ and Z are three more people, one a liar, one a switcher and one contrarian. They make the following statements:\\
$\mathrm { X } : \mathrm { Y }$ is the liar.\\
$\mathrm { Y } : \mathrm { Z }$ is the liar.\\
$\mathrm { Z } : \mathrm { X }$ is the liar.\\
$\mathrm { X } : \mathrm { Y }$ is the liar.\\
$\mathrm { Y } : \mathrm { X }$ is the liar.\\
Who is the liar among $\mathrm { X } , \mathrm { Y }$ and Z ? Briefly explain your answer.