Math 310
2–2–2009
Solutions to Problem Set 3
1. You visit an island where each person always tells the truth (a truth-teller) or always lies (a liar). You
meet two residents of the island, Calvin Butterball and Phoebe Small.
Calvin says: “Phoebe and I are both liars.”
Determine whether each person is a truth-teller or a liar, or whether the situation is impossible.
Suppose that Calvin is a truth-teller. Then his statement is true, and both of them are liars. In
particular, he’s a liar, which contradicts the assumption that he’s a truth teller.
Hence, Calvin must be a liar. Therefore, his statement is false. If Phoebe were a liar, then both would
be liars, and his statement would be true. Therefore, Phoebe must be a truth teller.
Thus, Calvin is a liar and Phoebe is a truth teller.
Nobody is bound by any obligation unless it has first been freely accepted. -Ugo Betti
c
2007 by Bruce Ikenaga 1