Before you read this, I should tell you that there are no REALLY cute girls in this bus post. (Well, there could be, if you want. Just replace every mention of "Bill" with "REALLY cute girl.")

I was reading a logic book, and I came across this problem. I could not solve all the questions after hours of effort, and so I ask now for you all to beat your brains out attempting to solve them, and then tell the manner of solution to me in exquisite detail.

_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.

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

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?

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

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

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

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

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I tried a Google search, and half of the few sites that turned up had a different premise: (3)(b) was changed to "Bill should not go home." The book I found it in is a logic book and has it the way found in the excerpt above, but it could still possibly be wrong. I made that error when copying it for the first time, and, also, one might note that, in all the other sentences, the contraction "shouldn't" is used instead of "should not." So maybe the book really is right and the internet sites are wrong.

gabby