#14 - Food labeling regulation: Food of a type that does not

[Steve Stein]

Hi Karen,

That's a good question—it's clear that the makers of the test don't go out of their way to be clear! Perhaps if we rearrange the order or presentation, this stimulus will become much easier to analyze. The whole statement deals with food that contains no fat. The first sentence provides that unless a food is generally mistakenly believed to have fat, it cannot be labeled "non-fat." Applying PowerScore's Unless Equation, this can be diagrammed as follows:

• labeled non-fat most people mistakenly believe it to have fat

• most people mistakenly believe it to have fat labeled non-fat

The second sentence is conditional as well, but the author makes things a bit confusing by presenting one sufficient condition at the beginning of the sentence and one at the end. Reordered, the second sentence simply provides that if most people mistakenly believe a food to normally contain fat, and the label states the food is ordinarily non-fat (basically correcting the misconception), the specific food can be labeled non-fat:

• most people mistakenly believe a food to have fat
  
  and food can be labeled non fat
  
  label states that the food is ordinarily non fat

The contrapositive of this conditional statement is as follows:


most people mistakenly believe a food to have fat

food can be labeled as non-fat or

label states that the food normally contains no fat

(if most people don't have such a mistaken belief about a given food, or if the label does not state that the food ordinarily contains no fat, then food cannot be labeled as non-fat.

Answer choice (D) violates these conditional rules, because labeling a food non-fat requires that most people mistakenly believe the food in question ordinarily contains fat.


Tricky question! I hope this is helpful--please let me know if this is clear--thanks!

~Steve

[karen_k]

Thank you Steve!

[nutcracker]

Hello,

Could anyone explain how answer choice (C) should be analyzed in the context of the food labeling regulation? This one looks like a rather ambiguous case to me. Thanks!

[Francis O'Rourke]

Answer choice (C) does not tell us whether Lester's Garlic Baguettes contain fat or not. Without that information, we cannot make a judgement on whether the 'nonfat' labeling of this product violates the rule or not.

[Pragmatism]

For the sake of clarity, and this stimulus does an amazing job at showcasing this, does the “if” in front of “most” imply that any conditional statement as such will have a contrapositive, whereas, a statement beginning with “most” wouldn’t? Also, if the stimulus had stated, “most people hypothetically could mistakenly believe that a food ordinarily contains fat,” then would it conotate the same meaning?

[Emily Haney-Caron]

Hi Pragmatism,

Thanks for the question! I'm not 100% sure what you're asking, and don't want to accidentally mislead you by misinterpreting your question. Would you mind explaining a bit more?

[Pragmatism]

Sure. So, this could possibly give you some pretext as to what my earlier post is seeking to clarify: when we have a “most” conditional statement, such as, “most As are Bs,” we can only deduce that most As are Bs. There is no contrapositve to a most statement. However, if we have a statement that is stated similarly to the statement in this stimulus beginning with “if most,” and using an example of “if most As are Bs,” then we can safely assume the contrapostive to be “those things that are not Bs are not mostly As” (hopefully I got that correct).

However, I was confused that how can an if conditional statement with most in it have a contrapostive, if most itself is the driving factor in the conditionality? Also, if most statements with “if” preceding it can have a contrapositive, then can a statement as, “Most people hypothetically could mistakenly believe that a food ordinarily contains fat, the food may be labeled “nonfat,” have the same effect in meaning as presented in the stimulus and also have a contrapostive being that the word “if” is being substituted for “hypothetically?”

[Shannon Parker]

Sure. So, this could possibly give you some pretext as to what my earlier post is seeking to clarify: when we have a “most” conditional statement, such as, “most As are Bs,” we can only deduce that most As are Bs. There is no contrapositve to a most statement. However, if we have a statement that is stated similarly to the statement in this stimulus beginning with “if most,” and using an example of “if most As are Bs,” then we can safely assume the contrapostive to be “those things that are not Bs are not mostly As” (hopefully I got that correct).

However, I was confused that how can an if conditional statement with most in it have a contrapostive, if most itself is the driving factor in the conditionality? Also, if most statements with “if” preceding it can have a contrapositive, then can a statement as, “Most people hypothetically could mistakenly believe that a food ordinarily contains fat, the food may be labeled “nonfat,” have the same effect in meaning as presented in the stimulus and also have a contrapostive being that the word “if” is being substituted for “hypothetically?”

Pragmatism,

A contrapositive is an inverse of conditional reasoning.The statement most As are Bs will not have a contrapositive because it is not a conditional statement. There is no set of conditions upon which one is relying for the other. Adding "if" can change this, but only if the conditional statement is completed. "if most As are Bs" does not have a contrapositive because it is not a complete conditional statement, it requires a necessary condition. For example "if most As are Bs, then most As are blue." The necessary condition of this statement is that most As are blue, and the sufficient condition is most As are Bs. (diagrammed as "most As are B's----> most As are blue"). The contrapositive of this statement would be if most As are not blue, then most As are not B.(diagrammed as "most As NOT blue, then most As not B").

The word "most" does not indicate a conditional statement and cannot be used to replace "if" in that context. In this stimulus the word "most" is simply part of the necessary condition indicated by the word "if,"most people mistakenly believe that a food ordinarily contains fat."

Hope this helps clear it up,
Shannon

[Pragmatism]

Yes it most certainly does. Thank you very much.

[jessicamorehead]

I've read through these explanations and have a couple questions.

I diagrammed it as follows:

food ordinarily does NOT contain fat: can be labeled NF most ppl believe it has fat

most ppl believe it has fat
AND can be labeled NF
label states food normally NF


I read that you can automatically eliminate A and B because they discuss foods that are "NOT labeled nonfat," but why is that? Is it because that fails the first conditional statement's sufficient condition? But what about the second conditional statement, couldn't that satisfy the CP of the second conditional statement? Can we eliminate these answer choices just for failing one of the conditional statements since they both have to hold true?

For C, I read that we can we eliminate it for talking about a "food with fat?" Does this fail the part of the first conditional statement which says, "food ordinarily does NOT contain fat?"

I see that E follows the rule, so that one is out. I also see how D violates the contrapositive of the first conditional statement, which is why it is the correct answer choice. However, I want to understand how to eliminate answer choices quickly on these types of questions.