Knight and Knaves logic problem

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.

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 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?