On an island each person always tells the truth or each person always tells a lie. Three people say $A$ , $B$ and $C$ have a conversation. $A$ says that $B$ is lying , $B$ says that $C$ is lying and $C$ says that both $A$ and $B$ are lying.
Then find out – who is lying and who is telling the truth.
So I have tried by supposition – For example let B be telling the truth- $$
\begin{array}{c|lcr}
n & \text{A} & \text{B} & \text{C} \\
\hline
& T & T& T\\
& \ & T & \
\
\end{array}
$$
What this means is if we assume $B$ to be true it implies that $C$ is true and that implies that $A$ is true and B is true . So there is a possiblity that $B$ is speaking the truth . I am thinking in this way…But am not going further about the Liars.
Best Answer
If $B$ lies, then $C$ is telling truth and hence $A$ lies which means $B$ is telling the truth and hence contradiction.
So if $B$ is telling the truth, then $C$ lies about $A$ and $B$. But also $A$ lies because $B$ is telling the truth. Hence: $B$ is telling the truth and $C$ and $A$ lie.
Note that if $C$ lies then either $B$ is telling the truth or $A$ is telling the truth.