Artificial intelligent assistant

Knight and Knave problem with 3 people. A says "All of us are Knaves". B says "Exactly one of us is a Knight". C says Nothing. In this problem the right solution we get from A and B will be the answer ? I get that A is Knave, B is Knight and C is Knave from A as Knave and B as Knight. Will this be the right answer ?

A cannot be a knight, for then they would all be knaves, including A.

So, A is a knave.

That means that they are not all knaves, and so at least one of B and C is a knight.

So, if B would also be a knave, then C is a knight ... the only knight ... so B is telling the truth ... which doesn't work. So: B is a knight.

Which means that there is exactly one knight, and hence C is a knave.

So yes: A is a knave, B is a knight, and C is a knave.

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