Conditional Possibilities vs. Certainties Drill p.2-58, 2-59

[wilu24]

I've tried this drill a couple of times and have a hard time comprehending how the correct answers were achieved for all of the problems but #5. I've been creating contra positives to come up with the answers, but maybe that's the wrong approach? In understanding Conditional Reasoning is it crucial to recognize all of the inferences as presented in the drill? (i.e. Must Be True, Could Be True, Cannot Be True)

[Lucas Moreau]

Hello, wilu,

The correct answers are all, fortunately, achieved through more or less the same method. It's all down to contrapositives and understanding how they work:

A B
Not!B Not!A

So for instance, number 1, if A B Not!C, and B does not occur (meaning Not!B), then we have to consider each of these two relationships.

A B
Not!B Not!A

B Not!C
C Not!B

So since we're told Not!B, we have to see if Not!B is a sufficient condition in either of those two relationships or their contrapositives. It is in the contrapositive of the first relationship. We know that if Not!B, then Not!A must be true. There is no way Not!A cannot occur (in other words, there is no way that A can occur) if Not!B occurs (if B does not occur).

As far as what could be true, we only know that Not!C occurs if B occurs. We know nothing about C if B does not occur (if Not!B occurs). So it could be true that C occurs, and it could be true that Not!C occurs.

It cannot be true, if Not!B occurs, that A occurs. Because if Not!B occurs, then Not!A occurs.

The same basic principles underlie the rest. If you give specific examples of what you were doing to create contrapositives, I or one of the other PowerScore tutors can help you more there.

Hope that helps,
Lucas Moreau

[wilu24]

Thanks Lucas. That explanation helped. I believe that I have been creating the contra positives correctly. I think my problem has been in how I view the conditions in relation to each other. The "not" element of the first problem is hard for me to think of in reverse, so I feel like that uncertainty caused me to have a block in understanding subsequent problems.