Knight and Knaves logic problem From "Discrete mathematics and its applications", a book by Kenneth H. Rosen,
chapter 1.1 exercise 57, goes as:


*A says "I am a knave or B is a knight" and B says nothing.


Knight always tell the truth and knaves always lie. We are to determine of which type are A and B.
Assuming that,
p: A is a knight
q: B is a knight 
Can I arrive to the answer (provided by the book), which is "A is a knight and B is a knight" using a truth table? And if not, then how?
 A: You don't even have to use a truth table. If A says that he is a knave or B is a knight, he cannot be a knave because if he was, then his statement would be true, even though knaves always tell lies. Now let's assume A is a knight. Then, since he isn't a knave, the second part of the statement, that B is a knight, must be true. So A and B are both knights.
A: Yes, you can do it with a four line truth table.  For each line assess the truth of $A$'s statement based on whether each is a knight.  Then see if the truth of the statement matches whether $A$ lies or tells the truth.
A: A truth table would help.  
In that table, there are four possible truths; (i) A and B are knights, (ii) A is a knight and B is a knave, (iii) A is a Knave and B is a knight, and (iv) A and B are knaves.
Let's proceed with testing whether (i) is true or false. If both A and B are knights, then the statement by A that "I am either a knave or B is a knight" cannot be refuted.
Next, let's test whether (ii) is true or false. If A is a knight and B is a knave, then the statement by A that "I am either a knave or B is a knight" cannot be true.  By hypothesis, A is a knight and is telling the truth.  So, A is not a knave and the statement by A must mean that B is a knight.  Inasmuch as B is a knave by hypothesis, we have a contradiction.  Therefore, the hypothesis that A is a knight and B is a knave is false.
Can you continue from here?
