Discrete mathematics, professor wants truth tables and proof by cases

(1) Suppose there are two neighboring islands, each of which is inhabited by knights and knaves (and no one else). You are told that on one of the islands there is an even number of knights, and on the other there is an odd number of knights. Also, you are told that there's gold on the island with an even number of knights, and that there's no gold on the other island. You visit one of the islands at random. All of the island's inhabitants know the number of knights and knaves there are living on the island. You encounter three inhabitants: A, B, and C, and they make the following statements: A: There is an even number of knaves on this island. B: Right now, there is an odd number of people on the island. C: I am a knight if and only if A and B are of the same type. Assuming that you are neither a knight or a knave and that at the moment you are the only visitor on the island, is there gold on the island or not