scharles,
The contrapositive is indeed as follows:
WH
S9
Because the original conditional and this conditional combine to tell you that WH and S9 cannot both be taken, you derive the following double not-arrow:
WH
S9
The setup never directly states that Alicia must take Statistics, so the negation of S9 isn't S3. Thus, your further inference that WH
S3 is
not the contrapositive of the original conditional. Instead, in order to infer that WH is sufficient to make S3 necessary, I would need first an inference (or a rule, but we lack one!) that said "Alicia must take Statistics." Without that inference, the mere fact that one Statistics cannot be taken does not lead to Alicia having to take the other; since there are 8 courses (6 + 2 different Statistics), and Alicia is taking only 4, we know she's not taking everything. So does she have to take Statistics?
What we need to consider here is whether she can do without Statistics. So we eliminate Statistics for the sake of a hypothetical, and consider whether she can take 4 of the remaining 6 courses.
Remaining courses: G, J, M, P, R, W.
By the last rule, one and only one of G/W can be taken, so one slot will be filled with the one course among this pair that she takes. So we have 3 slots for: J, M, P, R.
If she takes Psychology, she must take S9, which would put Statistics back in - we're trying to keep it out for our hypothetical! So P is gone, so the remaining 3 slots contain: J, M, R.
But M and J cannot be taken together by the second rule. So this doesn't work.
So some Statistics must be taken, which is the inference you wanted. Was this one you got on your own?
Robert Carroll
Post #1
