Q22 - If the budget does not allow for more dairy inspectors

[janie.love.williams]

Can someone explain the difference between answer choice D and A?
I'm sure it has to do with the contrapositive of the argument, but I'm not catching it.

Thanks in advance!

[christine.defenbaugh]

Great question janie.love.williams! This question is a wonderful illustration of some classic issues surrounding Sufficient Assumption questions!

As with any assumption family question, the first stop is to distill the core:

PREMISES
If no budget for more dairy insp --> most large dairies won't meet fed stds on waste disposal
There is no budget for more dairy insp
CONCLUSION
Most district water = likely to become polluted

Looking at our premises, we have one fact and one conditional. Since both of them have to be true, and the fact triggers the conditional - and that means the result of the conditional must be true as well! So, we can combine these two statements and properly conclude that most large dairies won't meet the federal standards.

So, we can simplify our core even further:

PREMISE
Most large dairies won't meet the fed stds on waste disposal
CONCLUSION
Most district water = likely to become polluted

Now, we need a Sufficient Assumption to guarantee that the argument works. Many times sufficient assumptions follow the classic pattern of:

IF (premise) THEN (conclusion)

The conditional relationship means that if the premise is true, the conclusion is guaranteed - that fulfills the job of a sufficient assumption!

(D) matches this classic pattern perfectly: IF (most large dairies won't meet the fed stds on waste disposal) THEN (most district water = likely to become polluted). This will guarantee the conclusion from the premise!

janie.love.williams, you are on target thinking that the problem with (A) has something to do with the contrapositive! In fact both (A) and (C) are examples of faulty translations (or faulty contrapositives) of this basic conditional.

BAD CONTRAPOSITIVE
(A) IF (most dairies meet fed stds for waste disposal) THEN (most district water = UNLIKELY to become polluted).
Illegal Negation. This negates both the trigger and the result of the conditional that we want. Our argument is about a world where most of the large dairies do not meet the federal standards - this answer choice tells us something about a world where most of them DO.

(C) Remember that "only if" translates to "then"! So the conditional is: IF (all district water = likely to become polluted) THEN (all large dairies do not meet fed stds for waste disposal).
Illegal Reversal. This format is IF (conclusion) THEN (premise). We needed to get from the premise to the conclusion, not the other way around!

WRONG FOR OTHER REASONS
(B) If this were true, then the fact that we can't get more dairy inspectors would mean we cannot possibly keep ALL the drinking water clean. So, at least some drinking water will get polluted. But that doesn't guarantee that MOST of the drinking water will get polluted!

(E) This gets to the right conclusion! But it only guarantees that conclusion if NONE of the large dairies meet the federal standards. We don't know that's true. The premises only tell us that MOST of the large dairies won't meet the federal standards. This conditional never gets tripped by our evidence!


Remember that a Sufficient Assumption has to guarantee that you can get from the premise to the conclusion!

I hope this helps clear things up a bit!

[AdjoaW937]

(C) Remember that "only if" translates to "then"! So the conditional is: IF (all district water = likely to become polluted) THEN (all large dairies do not meet fed stds for waste disposal).
Illegal Reversal. This format is IF (conclusion) THEN (premise). We needed to get from the premise to the conclusion, not the other way around!

Why is C considered wrong because it's an illegal reversal? Wouldn't it still be wrong even if it was the reverse given that we don't know about "all large dairies not meeting federal standards" but rather only "most"?

[Misti Duvall]

(C) Remember that "only if" translates to "then"! So the conditional is: IF (all district water = likely to become polluted) THEN (all large dairies do not meet fed stds for waste disposal).
Illegal Reversal. This format is IF (conclusion) THEN (premise). We needed to get from the premise to the conclusion, not the other way around!

Why is C considered wrong because it's an illegal reversal? Wouldn't it still be wrong even if it was the reverse given that we don't know about "all large dairies not meeting federal standards" but rather only "most"?

Good catch on the shift from most to all, but it's ok for sufficient assumption questions. For this type of question, the answer must be at least as strong as the conclusion, meaning it can be stronger. Never eliminate a sufficient assumption answer for being too strong.

[DominicE471]

(C) Remember that "only if" translates to "then"! So the conditional is: IF (all district water = likely to become polluted) THEN (all large dairies do not meet fed stds for waste disposal).
Illegal Reversal. This format is IF (conclusion) THEN (premise). We needed to get from the premise to the conclusion, not the other way around!

Why is C considered wrong because it's an illegal reversal? Wouldn't it still be wrong even if it was the reverse given that we don't know about "all large dairies not meeting federal standards" but rather only "most"?

Good catch on the shift from most to all, but it's ok for sufficient assumption questions. For this type of question, the answer must be at least as strong as the conclusion, meaning it can be stronger. Never eliminate a sufficient assumption answer for being too strong.

That is wrong! If you could go from "most" to "all" when referring to the dairies meeting the standards, then Choice E would be correct. All of the dairies not meeting the standards is equivalent to NONE of the large dairies meeting the standards which is what E says!!!