This is obviously elementary but can't figure it out. I am taking a course named Logic and Introduction to Analysis next semester and wanted to do some reading beforehand but to figure out how deep the course actually is, I looked through a previous exam paper. Everything else is pretty easy - mainly involving basic propositional logic. But this was the first question and I am stumped.
Consider the following conversation of four people:
$A : $ " $B$ always lies"
$B : $ " $C$ is a truth-teller"
$C : $ " $A$ told the truth"
$D : $ " None of $A, B$ and $C$ is a truth-teller"
$B : $ " Both $A$ and $C$ told lies"
How many are speaking truth in the conversation?
The options are None, One, Two, Three and Four.
How would I go about abstracting this?
Apologies everyone edited the last statement by $B$. Horrible mistake by me. Sorry.