Assuming the problem is exactly the same as it was in the book, none of the Q's can be logically extracted from the information given.

> _The Tardy Bus Problem_
>
> Given the following three statements as
> premises:
>
> (1) If Bill takes the bus, then Bill misses his
> appointment, if the bus is late.
>
> (2) Bill shouldn't go home, if (a) Bill misses
> his appointment and (b) Bill feels downcast.
>
> (3) If Bill doesn't get the job, then (a) Bill
> feels downcast and (b) Bill should go home.
>
> ...determine whether the following are valid to
> conclude:
>
> Q1: If Bill takes the bus, then Bill does get
> the job, if the bus is late.

No. The bus and whether or not Bill gets the job are not stated as being related.


> Q2: Bill does get the job, if (a) Bill misses
> his appointment and (b) Bill should go home.

No. The job is not stated as being related to the appointment, and nothing is said about what happens if he does get the job.


> Q3: If the bus is late, then (a) Bill doesn't
> take the bus, or Bill doesn't miss his
> appointment, if (b) Bill doesn't get the job?

No. It is not said that the bus' time of arrival has any effect on whether Bill takes it, and if the bus is late and he takes it then Bill does miss his appointment, and, again, Bill's job is not stated to have any relation to the bus or to his appointment.


> Q4: Bill doesn't take the bus, if (a) the bus
> is late, and (b)Bill doesn't get the job.

No. Again, the bus arrival time is not said to have an effect on whether Bill takes it, and neither is whether he gets the job.


> Q5: If Bill doesn't miss his appointment, then
> (a) Bill shouldn't go home, and (b) Bill
> doesn't get the job.

No. The appointment is not sead to have any bearing on his job, and it says nothing for what he should do if he makes his appointment.

> Q6: Bill feels downcast, if (a) the bus is
> late, or (b) Bill misses his appointment?

No. It does not say whether Bill's mood is affected by the bus' punctuality or whether he missees his appointment.


> Q7: If Bill does get the job, then (a) Bill
> doesn't feel downcast, or (b) Bill shouldn't go
> home.

No. While, if Bill does not get the job, he gets downcast and should go home, it is not said that the opposite is true -- he may very well be downcast or should go home, even if he gets the job.


> Q8: If (a) Bill should go home, and Bill takes
> the bus, then (b) Bill doesn't feel downcast,
> if the bus is late.

No. The bus may be late, even if Bill lost his job (and is therefore downcast).


I apologize if this isn't up to my usual standards of coherence (now there's a statement), but it is late at night.

-eric sleator
Fri 15 Jun A.D. 2001