A traveler in remote Quebec comes to a fork in the road and does

not know which way to go to get to Chicoutimi. Henri and Pierre

are two local inhabitants nearby who do know the way. One of

them always tells the truth, and the other one never does, but the

traveler does not know which is which. Is there a single question

the traveler can ask Henri (in French, of course) that will be sure

to tell him which way to go?

We will formalize this problem in FOL. Assume there are only two sorts of

objects in our domain, inhabitants denoted by the constants henri and pierre ,

and French questions , that Henri and Pierre can answer. These questions are

denoted by the following terms:

- gauche, which asks if if the traveler should take the left branch of the

fork to get to Chicoutimi;

-dit _oui ( x,q), which asks if inhabitant x would answer yes to the French

question q;

-dit_ non ( x,q), which asks if inhabitant x would answer no to the French

Question q ;

Obviously this is a somewhat impoverished dialect of French, although a

philosophically interesting one. For example, the term

dit_ non( henri. dit oui( pierre, gauche)))

represents a French question that might be translated as Would Henry answer

no if I asked him if Pierre would say yes I should go to the left to get to

Chicoutimi? The predicate symbols of our language are the following:

- Truth_ teller(x), which holds when inhabitant x is a truth teller;

-Answer_ yes(x,q), which holds when inhabitant x will answer yes to

French question q ;

-True (q ), which holds when the correct answer to the question q is yes;

-Go_left, which holds if the direction to get to Chicoutimi is to go left.

For purposes of this puzzle, these are the only constant, function, and predicate symbols.

Write FOL sentences for each of the following:

1- One of Henri or Pierre is a truth teller, and one is not.

2- An inhabitant will answer yes to a question iff he is a truth teller and the correct answer is yes, or he is not a truth teller and the correct answer is not yes.

3-The gauche question is correctly answered yes iff the proper direction is to go is left.

Please write correct answers in clear hand writing, otherwise type it