PT28.S1.Q2 - If the economy weak, prices remain constant...

_oshun1__oshun1_ Alum Member
edited March 2018 in Logical Reasoning 3652 karma

I don't get why answer choices D could be true. Are you not supposed to consider the contrapositives of the answer choices or of what's in the stimulus? I would think in this question you especially would want to consider the contrapositives since the last sentence calls for you to contrapose the entire stim to match with /ID. I thought that the explanation JY gave to A) would be applicable to D) as well.

https://7sage.com/lsat_explanations/lsat-28-section-1-question-20/

Stimulus:
EW → PC
EW→UR→ID

Contra: /ID →/UR→/EW
/PC→/EW

Answer choices:
D) /EW→PC. contra: /PC→EW. Not sure how it is that this CBT. In the stim, /PC --> /EW.

How can it be consistent to say that when prices aren’t constant, the economy is both weak and not weak o.O

Is it that, as long as either the contrapositive or original statement in the answer choice could be true, then the answer choice could be true? The original statement in D) could be true...

Admin note: edited title

Comments

  • Heart Shaped BoxHeart Shaped Box Alum Member ⭐
    edited March 2018 2426 karma

    Contra: /ID →/UR→/EW
    /PC→/EW

    Answer choices:
    D) /EW→PC. contra: /PC→EW. Not sure how it is that this CBT. In the stim, /PC --> /EW.

    The second part in D the contra form is not (/PC --> EW) but first CBT.

    You have it correct Contra form in stimulus: /PC --> /EW, but the first form (really the same form) of "D" /EW --> PC could be true, it doesn't contradict one of the logic chains in the stimulus: /PC --> /EW.

    Sorry I'm actually in the restaurant right now if anything is unclear I'll definitely try my best to clarify later. My apologies.

    Edit: Above comment is incorrect, I was drunk when writing it lol

  • Heart Shaped BoxHeart Shaped Box Alum Member ⭐
    edited March 2018 2426 karma

    Scratch the whole thing above lol i was only reading your translation earlier but after I looked at the question just now, I think I found the issue. Your contrapositive of the stimulus is incorrect. PC is a floater, hence /PC --> /EW is incorrect. We only know investment is not decreasing. My bad.
    A --> B --> C
    A --> F

    /C --> /B --> /A
    F floats, in this case price.

  • BinghamtonDaveBinghamtonDave Alum Member ⭐ 🍌🍌
    8716 karma

    This is a really tough question and I would have to defer to anyone that has studied logic to further elaborate any holes in my approach to this question.

    A MBF is something that cannot be true in any possible world. So if the stimulus gives us the conditional statement: A--->B--->C the MBF would be A and C.

    Because the "prices remain constant" element has no listed necessary conditions, the translation in (D) reading:
    EW--->PRC in fact could be true and therefore not a true MBF.

    I have never come across something like this again in LSAT history, but am open for correction on that.

    Now, there is another layer here: we are given a conditional chain and then we are told in reality we are failing one of our necessary conditions. Meaning we derive a "real fact" about the particular world in which the condition chain operates, the fact being that since investment is not decreasing, we run the contrapositive back to unemployment not rising and economy not weak. (A) MBF because it is expressing both in the given form and the contrapositive something that cannot be true.

    -David

  • _oshun1__oshun1_ Alum Member
    3652 karma

    @"Heart Shaped Box" said:
    Scratch the whole thing above lol i was only reading your translation earlier but after I looked at the question just now, I think I found the issue. Your contrapositive of the stimulus is incorrect. PC is a floater, hence /PC --> /EW is incorrect. We only know investment is not decreasing. My bad.
    A --> B --> C
    A --> F

    /C --> /B --> /A
    F floats, in this case price.

    PC isn’t a floater
    If economy is weak, prices are constant
    EW -> PC
    /PC -> /EW

    I’m just chalking it up to if either the contrapositive or original statement could be true then it’s not MBF

  • _oshun1__oshun1_ Alum Member
    3652 karma

    @BinghamtonDave said:
    A MBF is something that cannot be true in any possible world. So if the stimulus gives us the conditional statement: A--->B--->C the MBF would be A and C.

    Because the "prices remain constant" element has no listed necessary conditions, the translation in (D) reading:
    EW--->PRC in fact could be true and therefore not a true MBF.

    (A) MBF because it is expressing both in the given form and the contrapositive something that cannot be true.

    -David

    Thanks for breaking it down! I figured it was one of those all possible worlds situations

  • lsat4lifelsat4life Alum Member
    255 karma

    @BinghamtonDave said:
    This is a really tough question and I would have to defer to anyone that has studied logic to further elaborate any holes in my approach to this question.

    A MBF is something that cannot be true in any possible world. So if the stimulus gives us the conditional statement: A--->B--->C the MBF would be A and C.

    Because the "prices remain constant" element has no listed necessary conditions, the translation in (D) reading:
    EW--->PRC in fact could be true and therefore not a true MBF.

    I have never come across something like this again in LSAT history, but am open for correction on that.

    Now, there is another layer here: we are given a conditional chain and then we are told in reality we are failing one of our necessary conditions. Meaning we derive a "real fact" about the particular world in which the condition chain operates, the fact being that since investment is not decreasing, we run the contrapositive back to unemployment not rising and economy not weak. (A) MBF because it is expressing both in the given form and the contrapositive something that cannot be true.

    -David

    But the contrapositive is a restatement of the same relationship, isn't it? And the contrapositive of /EW -> PC is /PC -> EW, which seems to contradict the information given? So if we view "OR" statements as conditional relationship, we run into the problem OP found.

    I think an easier way to view this problem is that an "OR" statement is asserting that "at least one of these two things is true." And I think it's easier to see that EW is not true under the facts given, and that PC could be true. So that's why the "OR" statement could be true. I don't know if there is a difference between the statement "A or B" and the conditional version of it "/A -> B". Some people view them as exactly the same, but if they were, then we'd have OPs issue.

  • Heart Shaped BoxHeart Shaped Box Alum Member ⭐
    edited March 2018 2426 karma

    @"surfy surf"

    PC isn’t a floater
    If economy is weak, prices are constant
    EW -> PC
    /PC -> /EW

    True, if econ is weak, then prices are constant. But, we are never told PC, hence we can't take the contrapostive of PC --> EW, and that's where the issue lays.

    In the stimulus, we have:
    EW → PC
    EW→UR→ID

    But we are only told investment is not decreasing (ID) with which we would only get UR and EW, and in order to also take the contrapositive of PC, we need to be told PC, but we weren't, hence to take PC --> EW just bc of ID would be incorrect. PC is a true floater in this case.

    Therefore anything they say about PC could be true.

    D : either econ is weak or "PC constant", the latter could be true.

  • lsat4lifelsat4life Alum Member
    255 karma

    @"Heart Shaped Box" said:
    @"surfy surf"

    PC isn’t a floater
    If economy is weak, prices are constant
    EW -> PC
    /PC -> /EW

    True, if econ is weak, then prices are constant. But, we are never told PC, hence we can't take the contrapostive of PC --> EW, and that's where the issue lays.

    In the stimulus, we have:
    EW → PC
    EW→UR→ID

    But we are only told investment is not decreasing (ID) with which we would only get UR and EW, and in order to also take the contrapositive of PC, we need to be told PC, but we weren't, hence to take PC --> EW just bc of ID would be incorrect. PC is a true floater in this case.

    Therefore anything they say about PC could be true.

    D : either econ is weak or "PC constant", the latter could be true.

    (1) In order for any human to survive, he needs to eat. This means If S -> E. And If /E -> /S

    Based on (1), could the following statement be true?

    (2) If a human does not eat, he can still survive. (This seems like it cannot be true.)

    What about the following statement?

    (3) Humans must eat or they must survive. (This seems like a COULD be true.)

    The issue is that in some curriculum, (2) is seen as logically equal to (3). People diagram (3) as "If /E -> S". And yet the fact that (2) seems false, and (3) seems like a could be true suggests that there IS a difference in what they mean...

  • lsat4lifelsat4life Alum Member
    edited March 2018 255 karma

    This is a really fascinating question. Let me try to state it in even more basic terms.

    A -> B.

    In this world, it is a could be true that /A --> B. And yet, the contrapositive of this is /B --> A...which contradicts the initial claim, because according to the contrapositive of the initial claim, /B -> /A.

    Can a logic master make sense of this? Aren't contrapositives supposed to be expressing the exact same logical relationships?

    All dogs are cute.

    In this world, it's theoretically possible that Anything that is NOT a dog is cute. But is it possible that Anything that is NOT cute is a dog? Is it possible that Animals are either a dog or they are cute (or both)?

  • Heart Shaped BoxHeart Shaped Box Alum Member ⭐
    edited March 2018 2426 karma

    @thrillhouse
    Good question.

    A --> B

    From this I don't think we could conclude A --> B, the "conditional arrow" is the key here. We can say based on A --> B, it could be true that something not an A, (A) and yet we could still get a B: A and B, or A some B. But I don't think we could say A "implies" --> B.

    Therefore just from A --> B, neither A --> B nor B --> A is true.

    Same goes with "All dogs are cute"

    It could be true that something is not dog and yet still cute, D and C, or D some C, but it's not true that "anything" that's not a dog is cute. For example, my gf is not a dog, and I think she's pretty cute. Hence the conditional statement D --> C isn't true only based on D --> C.

    Edited: I had a brain fart above with my gf example, I meant to illustrate that it's not the case D --> C, the appropriate example would be: Hitler is not a dog, and I don't think he's cute.

  • lsat4lifelsat4life Alum Member
    255 karma

    @"Heart Shaped Box" said:
    @thrillhouse
    Good question.

    A --> B

    From this I don't think we could conclude A --> B, the "conditional arrow" is the key here. We can say based on A --> B, it could be true that something not an A, (A) and yet we could still get a B: A and B, or A some B. But I don't think we could say A "implies" --> B.

    Therefore just from A --> B, neither A --> B nor B --> A is true.

    Same goes with "All dogs are cute"

    It could be true that something is not dog and yet still cute, D and C, or D some C, but it's not true that "anything" that's not a dog is cute. For example, my gf is not a dog, and I think she's pretty cute. Hence the conditional statement D --> C isn't true only based on D --> C.

    Yes, I know. I was saying that A -> B leaves open the possibility that /A -> B. It doesn't imply /A -> B, though.

  • Heart Shaped BoxHeart Shaped Box Alum Member ⭐
    edited March 2018 2426 karma

    No it doesn't, and that's the key issue here. It cannot be true that A --> B just based on A --> B. The only possibility we have from that statement would be A and B or A some B, if we need to conclude B.

  • lsat4lifelsat4life Alum Member
    255 karma

    @"Heart Shaped Box" said:
    No it doesn't, and that' the key issue here. It cannot be true that A --> B just based on A --> B. The only possibility we have from that statement would be A and B or A some B, if we need to conclude B.

    Why is it impossible for /A --> B if we start with the fact that A --> B?

    Here is how I'm interpreting A -> B. "Whenever A is true, B is true."

    Given that fact, isn't it possible that "Whenever A is not true, B is true." In this situation, B is true all the time. And so if B were true all the time, then wouldn't it be correct to say that A --> B and also /A --> B?

  • Heart Shaped BoxHeart Shaped Box Alum Member ⭐
    edited March 2018 2426 karma

    @thrillhouse
    Let's look at it this way:

    "All cats drink milk"

    Yes, it could be true that something that's not cat can drink milk, (my dog) hence C and Milk or C some milk could be true. However, it's not true if we say "anything" that's not a cat drinks milk: C --> milk. The cell phone I'm using writing this comment right now isn't a cat, and it doesn't drink milk and the example list goes go.
    Hence it cannot be true that just from C --> milk, we conclude C --> milk

    Now, let's use your "whenever" example.

    "Whenever I'm happy, I study for the LSAT.
    Happy --> LSAT

    Yes, it could be true that if we say there are times I'm not really happy and yet I still study for the LSAT, hence happy and LSAT or happy some LSAT.
    But it's not true if we say "Whenever" I'm not happy, I study for the LSAT. I could be sad crying and going to bed, hence the conditional arrow cannot be drawn there, not from Happy --> LSAT.

    Back to your your example of "Whenever A is true, B is true.

    It could be true that sometimes when A is a not true, B is true. But it cannot be true if we say "Whenever" A is not true, B is true. Not from A --> B (I have a C that's not an A, and it's not a B )

  • lsat4lifelsat4life Alum Member
    edited March 2018 255 karma

    @"Heart Shaped Box" said:
    @thrillhouse
    Let's look at it this way:

    "All cats drink milk"

    Yes, it could be true that something that's not cat can drink milk, (my dog) hence C and Milk or C some milk could be true. However, it's not true if we say "anything" that's not a cat drinks milk: C --> milk. The cell phone I'm using writing this comment right now isn't a cat, and it doesn't drink milk and the example list goes go.
    Hence it cannot be true that just from C --> milk, we conclude C --> milk

    Now, let's use your "whenever" example.

    "Whenever I'm happy, I study for the LSAT.
    Happy --> LSAT

    Yes, it could be true that if we say there are times I'm not really happy and yet I still study for the LSAT, hence happy and LSAT or happy some LSAT.
    But it's not true if we say "Whenever" I'm not happy, I study for the LSAT. I could be sad crying and going to bed, hence the conditional arrow cannot be drawn there, not from Happy --> LSAT.

    Back to your your example of "Whenever A is true, B is true.

    It could be true that sometimes when A is a not true, B is true. But it cannot be true if we say "Whenever" A is not true, B is true. Not from A --> B (I have a C that's not an A, and it's not a B )

    But what if B is true all the time? In that case, then A -> B and /A -> B, (and C -> B and /C -> B). If B is true all the time, wouldn't any conditional that has B on the necessary side be a true statement? LIke, if I am literally studying for the LSAT 24/7, then it would be correct to say "whenever i'm happy, I am studying for the LSAT" AND "whenever I'm NOT happy, I am studying for the LSAT."

  • Heart Shaped BoxHeart Shaped Box Alum Member ⭐
    edited March 2018 2426 karma

    If B is true at all times, then it would be different statements without involving A. We just can't say from A --> B, therefore it could be true that A --> B.

    Same with studying for the LSAT 24/7 for the rest of our lives. Now, if that's the statement, then maybe we could say happy --> LSAT, and Happy --> LSAT, because someone literally studies for the LSAT 24/7 without doing anything else for the rest of their lives. In that case, anything could be pointing to the LSAT. But that's not our statement. Our statement isn't from "someone literally studying for the LSAT 24/7 forever," could it be true that Happy --> LSAT or Happy --> LSAT? Our statement is from Happy --> LSAT, can we say Happy --> LSAT? And the answer is no. We just can't say from Happy --> LSAT, therefore Happy --> LSAT, nor from Happy --> LSAT, it could be true that happy --> LSAT.

    Here is another way of looking at it:

    A --> B

    True, if we failed the sufficiency, we could still get the necessary. A some B. However, that's different from anytime or anything that failed suffiency will get us the necessary. A --> B.

  • akistotleakistotle Member ⭐ 🍌🍌
    edited March 2018 9382 karma

    @"surfy surf"

    This is a really hard question!

    EW → PC.
    EW → UR → ID
    /ID
    -------------
    /EW, /UR

    I think the point here is that the premise doesn't give us /PC.

    If it said so, it would be /PC and /EW. And (D) would contradict because it says /PC → EW, so it must be /PC and EW.

    (A): /EW → ID (= /ID → EW)
    This is inconsistent with the premise /ID and /EW; therefore must be false.

    (D): /EW → PC (= /PC → EW)
    This is consistent with EW → PC. (/PC → /EW). It could be false but does not have to be false. Under this conditional statement (/EW → PC), (1) /EW and PC, (2) /PC and EW, (3) EW and PC could happen. The premise doesn’t say /PC.

    With (D) [=/EW → PC], what we know is that we can't have /PC because it would lead to contradiction. So we know it must be PC.

    /PC → EW [Answer choice (D)]
    /PC → /EW
    -------------
    PC

    This reminds me of the infamous inference on "two clinics: Souderton or Randsborough" game (PT34.S4.Game 4)
    https://7sage.com/lsat_explanations/lsat-34-section-4-game-4/

  • Heart Shaped BoxHeart Shaped Box Alum Member ⭐
    2426 karma

    @akistotle said:

    I think the point here is that the premise doesn't give us /PC.

    @akistotle nailed it. We are never told PC.

    This reminds me of the infamous inference on "two clinics: Souderton or Randsborough" game (PT34.S4.Game 4)
    https://7sage.com/lsat_explanations/lsat-34-section-4-game-4/

    That was a great game, lots to learn from!

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