0:05

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

Â let's consider the following problem.

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

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

Â 0:26

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Â the concepts we have seen so far.

Â