If the concrete is poured while the ground is wet, it will not form a solid foundation. If the concrete does not form...

Naz on October 29, 2014

Alright let's diagram:

"If the concrete is poured while the ground is wet, it will not form a solid foundation."

P1: PGW ==> not FSF
FSF ==> not PGW

"If the concrete does not form a solid foundation, it will either settle unevenly or crack."

P2: not FSF ==> SU or C
not SU and not C ==> FSF

"So if the concrete settles evenly, either it was poured while the ground was dry or it will crack."

C: not SU ==> not PGW or C
PGW and not C ==> SU

So, the argument takes one of the sufficient conditions of the contrapositive of P2 to conclude either "not PGW" or "C". How does it do this?

Well it takes "not SU" and then shows what would happen in the dichotomy of having "C" and having "not C." Okay, so taken together, if it cracks, then we have "not SU" and "C" together. If it doesn't crack, then we have "not SU" and "not C" together. Having "not SU" and "not C" together will trigger the contrapositive of P2 to infer "FSF," which triggers the contrapositive of P1, which triggers "not PGW."

So in our dichotomy, when we have "not SU," we will also either have "not PGW" or "C."

Now let's diagram answer choice (A):

"The film will not be properly exposed if the camera is not working properly."

P1: not WP ==> not PE
PE ==> WP

"If the film is not properly exposed, then the photograph will be either blurred or dark."

P2: not PE ==> B or D
not B and not D ==> PE

"So if the photograph is not blurred, either the camera is working properly or the photograph will be dark."

C: not B ==> WP or D
not WP and not D ==> B

Similarly, this answer choice sees what happens when we have "not B" and the dichotomy of having "not D" and having "D."

So, we can either have a photograph be not blurry and dark, which wouldn't trigger anything because "D" is not a sufficient condition, or we can have a photograph be not blurry and not dark (not B and not D), which triggers the contrapositive of P2 to infer "PE," which triggers the contrapositive of P1 to infer "WP." Therefore, if a photograph is not blurry, it will either be "D" or "WP."

So, as you can see, the argument and answer choice (A) have the same reasoning.

Hope that clears things up! Please let us know if you have any other questions.