In the 1960s, the Mathematician, Logician, and Puzzle Wizard (also happens to be a remarkable Gandalf looka-like) Raymond Smullyan began posting many...

In the 1960s, the Mathematician, Logician, and Puzzle Wizard (also happens to be a remarkable Gandalf looka-like) Raymond Smullyan began posting many (logic) puzzles and the general population fell in love with them. Many of these puzzles reference an island that has two kinds of inhabitants, knights, who always tell the truth, and their opposites, knaves, who always lie. (For people interested in politics replace these with your particular party affiliation.)

Problem 1. Suppose you find yourself on an island that has two kinds of inhabitants, knights, who always tell the truth, and their opposites, knaves, who always lie. You encounter two people A and B.

(1) What are A and B if A says "B is a knight" and B says "The two of us are opposite types?"

(2) What are A and B if A says "The two of us are both knights" and B says "A is a knave."