That's logic, that is

That's logic, that is
You meet three people, A, B and C. Each of them is a knight (always tells the truth), or a liar (always lies) or a knave (alternates between telling the truth and lying, although you don't know which they do first). You ask them what they are and they reply as follows.

A: I'm a knight.
B: No you're not!
C: Well, I'm a liar.
A: I agree, you are.
B: Bullshit. I disagree.
C: You're right, B, as always.

Alrighty then. Explanation.

If someone is a knight, they'll say they're a knight. If someone is a liar, they'll say they're a knight or a knave. If someone is a knave, they could say anything. Therefore the only type of person who could say they're a liar is a knave, who is lying.

Therefore C is a knave, whose first statement is false and second statement is true.

If C's second statement is true, B is telling the truth, and is always telling the truth (C's last statement). Therefore B is a knight.

A is not a knight, because B said so, so A's first statement is false. A's second statement is false too because C is not a liar, therefore A is a liar.

Summary: A is a liar, B is a knight and C is a knave.

That wasn't too bad, was it?