Page 2-58 Problem # 1 Chapter 2 Part two

[brown117]

I was working on a drill for review and reviewing the answers in the book. I understood and got the first part right but I did not understand why the correct answers were correct for part two of the question. Was it because part two continued to operate off the premise that B does not occur as it did in the first part of the problem? Can someone help me?

A B C

If B does not occur, what:
Must be true: A does not occur
Could be true: C occurs: C does not occur
Cannot be true: A occurs

If C occurs, what:

Must be true: B does not occur; A does not occur
Could be true:
Cannot be true; B occurs; A occurs

[Luke Haqq]

Hi! Hopefully I'll be able to help. First off, it looks as though you have question one reproduced without C being negated (I'll represent negation with "~"). It should read:

A B ~C

Your question is particularly about the second part.

If C occurs, what must be true, could be true, and cannot be true?

To answer these questions, try taking the contrapositive of the first statement:

C ~B ~A

This has to be true, given the first statement. If you have C, you can have neither B nor A. Once we have this contrapositive, we can return to the three questions. What

Must be true? B and A do not occur
Could be true? --
Cannot be true? B and A occur; C does not occur.

[brown117]

Thank you so much. After reading your comment I had to go back and look at my book again. I have done the problems so many times and left so many marks I could not tell what the original problems stated. Thank you again