You find yourself in a maze walking and you reach a 3-way intersection. The roads have...

You find yourself in a maze walking and you reach a 3-way intersection. The roads have signs as follows: -on the left: “bad idea street” -in front of you: “don’t even try it road” -on the right: “you’re lost avenue” On each one of the roads there is a street vendor (hey, it’s Miami, they are everywhere!). You talk to the street vendors and this is what they tell you (after you buy some of their goods of course): -Street vendor on “bad idea street”: “This road will take you straight to Cold Stone Creamery. Also, if “you’re lost avenue” leads you to Cold Stone Creamery, then “don’t even try it road” will also take you to Cold Stone Creamery.” -Street vendor on “don’t even try it road”: “Neither “bad idea street” nor “you’re lost avenue” takes you to Cold Stone Creamery.” -Street vendor on “you’re lost avenue”: “Follow “bad idea street” and you’ll reach Cold Stone Creamery. Furthermore, follow “don’t even try it road” and you will never leave this maze (Muahaha).” It is common knowledge that street vendors never tell the truth. Furthermore, you are dying for some ice-cream, after a whole day of being lost in the maze. Can a road be chosen (with 100% certainty) such that it will take you to your neighborhood Cold Stone Creamery? If it can be done, which road would you choose? Provide formal language and propositional logic facts (propositions) that formalize the problem and prove(show steps) whether a road can be chose so that you can be sure it will lead you to Cold Stone Creamery(for some yummy ice-cream).

Expert Solution

Answer:-

Answer is You are Lost Avenue

Explanation:

Known Facts: Vendors never say Truth.

Case1: Vendor on "bad idea street", "bad idea street" leads to CSC (Cold Stone Creamery). Also, if “you’re lost avenue” leads you to CSC, then “don’t even try it road” will also take you to CSC.”

a) Conclusion1 from Case1: As we know that he is saying lie, Therefore "bad idea street" will not lead to CSC.

b)Conclusion2 from Case1: It is lie, so if “you’re lost avenue” leads you to CSC, then “don’t even try it road” will not take you to CSC.”, This means either “you’re lost avenue” or “don’t even try it road” will lead to CSC.

Case2: vendor on “don’t even try it road”: “Neither “bad idea street” nor “you’re lost avenue” takes you to CSC.

a) Conclusion 3 from Case 2: Either “bad idea street” or “you’re lost avenue” alone takes you to CSC.

Case3: vendor on “you’re lost avenue”: Follow “bad idea street” and you’ll reach Cold Stone Creamery. Furthermore, follow “don’t even try it road” and you will never leave this maze.

a) Conclusion 4 from case 3: “bad idea street” will not lead to CSC.

From all the above conclusions, we can say that only “you’re lost avenue” leads to CSC.

Colby Messinger answered 2 years ago

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