Aice, Bob, and Chloe are perfect logicians. Each can instantly deduce all consequences of any set of premises; each is a

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Aice Bob And Chloe Are Perfect Logicians Each Can Instantly Deduce All Consequences Of Any Set Of Premises Each Is A 1 (163.22 KiB) Viewed 34 times

Aice, Bob, and Chloe are perfect logicians. Each can instantly deduce all consequences of any set of premises; 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. We make the following three propositional variables r1 = "Alice's hat is red” r2 = “Bob's hat is red” rz = "Chloe's hat is red” Alice's blindfold was first removed and she was asked, “Do you know one color that you definitely do not have?” She replied, “No." a) Bob's blindfold was then removed and he was asked the same question and he replied, “No.” Can Chloe deduce the color of her hat based on Alice and Bob's answers? Hint: Chloe learns some extra information from Bob's 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? Note that Chloe should be thinking from Bob's point of view. b) After all, can Alice or Bob figure out the color of their hats? If not, how many options are there for the color of their hats? What are the options?