In an islander problem, we are given a set of statements that are about one another. Each of a set of islanders makes a statement about the truth or falsity of their own or other islanders' statements. Each statement is either true or false, so we have a set of compound propositions with an atomic variable for each. Normally the problem is set up so that exactly one setting of the variables matches the variables. That is, each statement whose variable is set to true becomes true, and each one set to false becomes false. Given the following situations, which islanders, if any, are telling the truth? (a) There are two islanders. A says "Exactly one of us is lying". B says "If A is telling the truth, then so am I." (b) There are three islanders. A says "It is not the case that both the other two are telling the truth." B says "At least one of the other two is telling the truth." C says "A is telling the truth, and if B is telling the truth then so am I."