Please, I neeed a help in this discrete math question. Portia’s Caskets (PV 2006
ID: 3880217 • Letter: P
Question
Please, I neeed a help in this discrete math question.
Portia’s Caskets (PV 2006)
In Shakespeare’s Merchant of Venice, Portia had three caskets, gold, silver and lead, inside one of which was her portrait. Her suitor was asked to choose one of the caskets, and if he chose the portrait, he could claim Portia as his bride. Here is Portia’s casket test again with a twist. Suppose there are two casket makers, Bellini and Cellini.
Bellini always writes true statements on his caskets, while Cellini always writes false ones.
(a) Suppose one of the caskets contains, not a portrait, but a dagger, and the suitor’s job is to avoid choosing that casket. The caskets are inscribed as follows:
Gold: The dagger is in this casket.
Silver: This casket is empty.
Lead: At most one of these three caskets was made by Bellini.
Which casket should the suitor choose? Explain your answer.
(b) Suppose Portia placed her portrait in one of the caskets and the suitor’s job is to select the casket with the portrait and to determine the maker of each of the three caskets. The caskets are inscribed as follows:
Gold: The portrait is in here.
Silver: The portrait is in here.
Lead: At least two of these caskets were made by Cellini.
How should the suitor answer to pass the test? Explain
Explanation / Answer
(a) Suppose Lead Box statement is written by Cellini, then the rest two would have statements written by Bellini. In that case Gold Box will have dagger and Silver will be empty and therefore Lead Box contains portrait.
Suppose the Lead Box Statement is written by Bellini, in that case the Lead Box would be maade by Bellini and the rest two would be made by Cellini. Therefore Gold will not have dagger and Silver box will also be not empty. Dagger would be in Silver or Lead Box. Similarly Gold or Lead Box can be empty, we do not have enough assertions to be made to find out which box has portrait.
Hence, we would go with first option and suitor must choose Lead Box.
(b) Suppose Lead Box is made by Bellini then in that case Gold and Silver Box would be made by Cellini. Therefore both the Gold and Silver Boxes does not contains Portrait and hence Lead Box Contains the portrait which is made by Bellini.
If the Lead Box is made by Cellini, then the statement written on it must be false and its opposite would be at most one made by Cellini which is Lead Box and rest the other two boxes would have made by Bellini and which is not the ideal case when two boxes contains the portrait.
Therefore, Lead Box contains the portrait which is made by Bellini.