There is an island that has two kinds of inhabitants: knights, who always tell the truth, and knaves, who always lie. You encounter two inhabitants of the island, A and B. A says: At least one of us is a knave. What are A and B?

Let p be the statement A is a knight and q be the statement B is a knight.

Solve Using Rules of Inference for Propositional Logic:

Question) Assume that A is a knight. Use the rules of inference to determine whether B is a knight or a knave.

p

p q

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q

I was able to quantify the hypotheses and this is the conclusion just how do I come to this conclusion.