Suppose that you meet three people, Anita, Boris, and Carmen. What are Anila, Boris, and Carmen if Anila says "I am a knave and Boris is a knight" and Boris says "Exactly one of the three of us is a knight"?

Solution:

Step 1:

In this problem we need to determine what exactly they are.

Given: Anita says “I am a knave and Boris is a knight” and Boris says “Exactly one of the three of us is a knight”.

We know that knight always tell the truth and knave always tell the lie.

Let us assume that, Anita says “I am a knave and Boris is a knight” is true.

So, Anita is a knave.But we know that knave always tell the lie.So, the second statement Boris is a knight is false.

Hence, Boris must be a knave.

Therefore, Anita is a knave and Boris is a knave.