Aice, Bob, and Chloe are perfect logicians. Each can instantly deduce all consequences of any set of premises. Also, each is aware that each of the others is a perfect logician. The three were shown five hats: two red ones and three blue ones. They were then blindfolded, and a hat was placed on each of their heads; the remaining two hats were placed in a drawer. Alices blindfold was removed and she was asked, Do you know one color that you definitely do not have? She replied, No. Then Bobs blindfold was removed and he was asked the same question and he replied, No. Is it possible, from the above information, for Chloe to deduce the color of her hat, even while still blindfolded? To answer the question, Chloe makes the following three propositional variables r1 = Alices hat is red r2 = Bobs hat is red r3 = Chloes hat is red

c) (10 points) Chloe learns some extra information from Bobs answer when his blindfold is removed. What can Chloe figure out about r3 (the color of her own hat) using all of the above information?