An exercise from the book A Mathematical Introduction to Logic

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SUMMARY

The discussion revolves around a logic puzzle from "A Mathematical Introduction to Logic," where a traveler must determine which fork in the road leads to the capital by asking a local resident one yes-or-no question. The proposed solution involves asking, "If I asked you 'does the right way lead to the capital?', would you answer 'yes'?" This question effectively accounts for the truth-teller and liar scenarios, ensuring that a "yes" response indicates the right fork and a "no" indicates the left. Additionally, participants discuss the suggestion to "make a table" to visualize the outcomes based on the truthfulness of the resident.

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  • Understanding of logical reasoning and truth tables
  • Familiarity with propositional logic concepts
  • Basic knowledge of logical puzzles and paradoxes
  • Ability to analyze conditional statements
NEXT STEPS
  • Study truth tables in propositional logic
  • Explore logical paradoxes and their resolutions
  • Learn about the implications of asking conditional questions
  • Investigate other logic puzzles involving truth-tellers and liars
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Students of logic, puzzle enthusiasts, educators teaching logical reasoning, and anyone interested in problem-solving strategies involving conditional statements.

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Homework Statement



you are in a land inhabinated by people who either always tell the truth or always tell falsehoods. You come to a fork in the road and you need to know which fork leads to the capital. There is a local resident there, but he has time only to reply to one yes-or-no question. What one question should you ask so as to learn which fork to take?
suggestion: Make a table.


Homework Equations





The Attempt at a Solution



If I asked you 'does the right way lead to the capital?', would you anwser 'yes'?
If the guy reply yes, take the right way. If no, the left.

I am wondering if I am surposed to ask questions about 'future' here?
What exactly does the writer mean by 'make a table'?
 
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That's a perfectly good answer. As far as "make a table", I suspect it refers to having two columns, whether the right or fork is correct, and two rows, whether the person tells the truth or lies, when considering what results a specific question would get.
 

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