If a mechanical aerator is installed in a fish pool, the water in the pool can be properly aerated. So, since John's...

Charmaine on February 6, 2015

Diagramming this is confusing

Not sure how to diagram this answer choice! I realized quickly that it wasn't Answer Choices C,D, or E. But A confused me totally.

1 Reply

Melody on February 10, 2015

Alright let's diagram this:

"If a mechanical aerator is installed in a fish pool, the water in the pool can be properly aerated."

P1: IFP ==> PA
not PA ==> not IFP

"So, since John's fish pools does not have a mechanical aerator, it must be that his pool is not properly aerated."

P2: not IFP ==> not PA
PA ==> IFP

"Without properly aerated water, fish cannot thrive."

P3: not PA ==> not FT
FT ==> PA

"Therefore, any fish in John's pool will not thrive."

C: not FT

The issue here is that "P2" is a sub-conclusion made erroneously by confusing the sufficient and necessary conditions. Just because John's fish pool does not have a mechanical aerator, does not mean that is pool is not properly aerated. We merely know that is a mechanical aerator is installed in a fish pool, then the water in the pool can be properly aerated.

Thus, we cannot use it, as the argument has, to make its conclusion.

Answer choice (A) contains the same flawed reasoning as in the argument. It is, therefore, diagrammed similarly:

"If alum is added to pickle brine, brine can replace the water in the pickles."

P1: AAPB ==> BRW
not BRW ==> not AAPB

"Therefore, since Paula does not add alum to her pickle brine, the water in the pickles cannot be replaced by brine."

P2: not AAPB ==> not BRW
BRW ==> AAPB

"Unless their water is replaced with brine, pickles will not stay crisp."

P3: PSC ==> BRW
not BRW ==> not PSC

"Thus, Paula's pickles will not stay crisp."

C: not PSC

Just as in the argument, "P2" is a flawed sub-conclusion made by confusing the sufficient condition for the necessary condition. We cannot just negate the conditions; we must negate AND reverse to make a correct contrapositive.

Thus, just because Paula does not add alum to her pickle brine, we cannot conclude that the water in the pickles cannot be replaced by brine. We only know that if alum is added to pickle brine, the brine can replace the water in the pickles.

Therefore, just as in the argument, we cannot use "P2" to make our conclusion.

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