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Finally as an exercise in using some of the concepts introduced in this section,

let's consider the following problem.

Stanford people always tell the truth and Berkeley people always lie.

Unfortunately, by looking at a person you cannot tell whether he is from Stanford or Berkeley.

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You come to a fork in the road and want to get to the football stadium down one fork, or you did not know which road to take.

There is a person standing there. What single question can you ask him to help

you decide which fork to take? There are a number of ways to approach this problem

most interesting involves a question in which a person is asked. How we would

answer if you were from Stanford or if you were from Berkley. However, we can also

approach this problem without entertaining such meta-level questions. Let's draw out

a table with the set of all possible states of affairs, and leave columns for

the question we want to ask and the response we want to receive. We want to ask a

question that will list of one response. Let's say true or one, if the stadium is

to the left, and a different response, For example, false or zero, if the stadium is

to the right. Note that the response in each case may differ from the actual

truth of the question depending on whether the informant is from Stanford or from

Berkley. Now, let's see what the actual truth value or question must be to have

elicited this response. If the stadium is actually to the left, and the informant is

actually from Stanford, then we want a question that has value true. If the

stadium is not to the left, and the informant is from Stanford, then we want a

question with truth value false. So it stands that if a person's going to tell

the truth the value should be the same as the values in our response. The opposite

is true for the Berkley case, cases, if the stadium is to the left and the

informant is from Berkley, we want a question the has truth value of false

since the informant were lying. If the stadium is not to the left and the

informant is from Berkeley then we want a question that has truth value true. Now looking

at our operator semantics tables, we see that this is exactly the set of true

values assigned to the sentence left, if and only if SU, Stanford. So we can phrase

this as a question as follows. Is it the case that the left road is the way to the

stadium if and only if you are from Stanford. Okay, that's not a particularly

clever or simple question, but it will ellicit the right response. Importantly

the example illustrates that it's possible to solve problems of this sort using just

the concepts we have seen so far.