need help with negating sentences for necessary assumption

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• 1 Like

  cal6005 Free Trial Member

  July 2016 106 karma

  The LSAT Trainer says that the negation test means taking the "exact opposite" of the statement. From the examples you included, I assume that you're having trouble figuring out which part of the statement to negate in If/Then statements. By "exact opposite," I just take this to mean that the negated sentence will imply the opposite meaning/outcome of the original sentence. So for example, if I said "If a dog is sick, it will seem tired and lazy," the negated statement would be "If a dog is sick, it will NOT seem tired and lazy" (not "If a dog is NOT sick, it will seem tired and lazy"). Does that make sense? Then, if the negated statement severely weakens or destroys the argument, then the original statement is a necessary/required assumption.
  
  So, for your 1st statement, I would take "The Fine arts would be more highly developed now if they had been given greater governmental subsidies in the past" and negate it to say "The Fine arts would NOT be more highly developed now if they had been given greater governmental subsidies in the past."
  
  For the 2nd statement, I'd take "If contemporary governments help to maintain and enrich the fine arts, private support for the arts will become necessary" and negate it as "If contemporary governments help to maintain and enrich the fine arts, private support for the arts will NOT become necessary."
  
  For the 4th statement, I'd take "Serving as stewards of cultural heritage requires that contemporary societies help to maintain the fine arts" and negate it as "Serving as stewards of cultural heritage DOES NOT require that contemporary societies help to maintain the fine arts."
  
  For the 5th statement, I'd take "Maintenance, advancement, and enrichment of the fine arts in any era require governmental subsidies" and negate it as "Maintenance, advancement, and enrichment of the fine arts in any era DOES NOT require governmental subsidies."
  
  In your 3rd statement, I think you have the right idea that to negate the statement, you should remove NOT.
  
  I don't know if this will help at all but I hope it does!
• stepharizona Alum Member

  July 2016 3197 karma

  For me the "It is not the case that"... Before every NA answer helped me with negation.
  
  So It is not the case that maintenance, advancement, and enrichment of the fine arts in any era require governmental subsidies.
• blah170blah Alum Inactive ⭐

  July 2016 3545 karma

  Necessary assumption questions are one of my few strengths in LR and I rarely diagram. I always think: "what would need to be true for this claim to be correct?" The answer to that question is the necessary assumption.
  
  S1: In order for this claim to be true, there has to be a positive relationship between government subsidies and improvement in fine arts. (Otherwise, why would we expect fine arts to improve with government subsidies?)
  
  S2: In order for this claim to be true, there is no other substitute for private support of the arts (Otherwise, why would it be necessary?)
  
  S3: I'm not entirely sure how this is an argument with an assumption without it providing some reason for why we believe contemporary societies aren't helping the arts.
  
  S4: In order for this claim to be true, nothing else serves stewards of cultural heritage (otherwise, why MUST we need societies thy maintain)
  
  S5: In order for this claim to be true, nothing else will maintain, advanced and enrich the fine arts (otherwise, why MUST we need subsidies?)
  
• 2 Likes

  quinnxzhang Member

  July 2016 edited July 2016 611 karma

  @cal6005 said:
  So for example, if I said "If a dog is sick, it will seem tired and lazy," the negated statement would be "If a dog is sick, it will NOT seem tired and lazy"
  

  This is incorrect. The negation of 'A → B' is '~(A → ', or equivalently 'A & ~B'. So the negation of "If a dog is sick, it will seem tired and lazy" is "A dog is sick and will not seem tired and lazy".
  
  Similarly for the rest of the negations in your comment.
  
  ***Admin Edit***
  Here are some of the relevant lessons:
  https://7sage.com/lesson/advanced-negate-all-statements/
  https://7sage.com/lesson/deny-the-relationship/
  
• cal6005 Free Trial Member

  July 2016 106 karma

  @quinnxzhang, no hostility implied here, but I don't understand the point of the negation you made. It's definitely possible that I'm wrong, as I often am, but the explanation I gave has worked for me to get the correct answer for every necessary assumption question I've seen since I read the Trainer. For me, it makes more intuitive sense to not break things down into symbolic conditional statements and formulas and just think it through in the context of the sentence's original meaning in the English language, and the sentence you ended up with hardly makes sense to me (A dog is sick and will not seem tired and lazy). Like, the dog IS currently sick, but WILL NOT in the future seem tired and lazy? Why not use "does not seem?" To me it reads as two different tenses and is confusing for no reason.
  
  I just don't understand the point in making this more complicated than it needs to be. The point of the negation test for necessary assumption questions is to check if the original statement is required by the argument. The sentences "A dog is sick and will not seem tired and lazy" and "If a dog is sick, it will NOT seem tired and lazy" mean the same thing in my mind except that the sentence you provided makes little sense and is no longer a conditional statement. It's possible that the correct negation would be "If a dog is sick, it WON'T NECESSARILY seem tired and lazy," but I feel like for the purpose of finding the correct answer to a necessary assumption question it's faster to just think of the opposite of the original sentence. And just personally, I'd rather work with sensical statements than symbolic statements when I only have a minute to figure out the answer to a question. Also, like what @stepharizona said, it is also possible to just add "it is not the case" or "it isn't true that" before the statement, but to make the sentence have the opposite meaning, I think you can just add a "not."
  
  If I'm truly wrong here, I'd like to know so that I can stop using this method when I'm studying.
• blah170blah Alum Inactive ⭐

  July 2016 3545 karma

  @cal6005 Your negation statements seem to make sense and if it works for you, that's great. I would just advise keeping the nuance of "WONT NECESSARILY" in your mind because the answer choices of later necessary assumption questions will prey on that mental shortcut.
• rachel Alum Member

  July 2016 207 karma

  When @quinnxzhang shows the negation using conditional diagrams, I believe he is simply showing that the negation of a conditional statement results in two conditions NO LONGER having a conditional relationship with each other. In other words, you can have one without the other. The negation of the dog statement using the ~(A > method that he showed means that you can have a sick dog and it will not necessarily be tired and lazy. You can have A without having B, whereas previously, if you had A, you necessarily had B.
• quinnxzhang Member

  July 2016 edited July 2016 611 karma

  @cal6005, regardless of whether your method worked for you in the past, it's straightforwardly incorrect. It's very important to understand that the negation of "If P then Q" is NOT "If P then not Q". This is a major mistake! I say that with no hostility either.
  
  I would also caution against putting too many eggs into your intuitions basket. If the LSAT has taught you anything, hopefully it's taught you that our intuitions are often fallible, and saying "it makes sense" shouldn't be sufficient.
  
  Part of the problem is that LSAT courses don't teach predicate logic, so students often get confused about how to properly negate statements involving quantifiers. Unfortunately, 7sage is no better here. Your example sentence is actually a quantified sentence, but I simplified it into propositional logic because the latter is the only thing covered in LSAT courses.
  
  To be precise, your sentence, "If a dog is sick, it will seem tired and lazy", actually expresses the following proposition: Every dog is such that if it's sick, it will seem tired and lazy. The negation of this is: Some dog is such that it's sick and will not seem tired and lazy. Why?
  
  Recall that not all is equivalent to some not. So "not every dog is such that if it's sick, it will seem tired and lazy" is equivalent to "for some dog(s), it's not the case that if it's sick, it will seem tired and lazy". Recall that "if P, then Q" is equivalent to "not P or Q". So substituting this equivalence in, we get "for some dog, it's not the case that (it's not sick or it will seem tired and lazy)". And, lastly, applying De Morgan's to the embedded negation, we get "for some dog, it is sick and will not seem tired and lazy". This is what I expressed when I wrote "a dog is sick and will not seem tired and lazy" in my first comment, and now you see why it's in fact the correct negation of your example sentence.
• 3 Likes

  MrSamIam Inactive ⭐

  July 2016 2086 karma

  Think of negations like you would if someone asked you to provide them with the opposite of a given statement.
  
  1)The Fine arts would be more highly developed now if they had been given greater governmental subsidies in the past.
  
  The fine arts would not be more highly developed now even if they had been given greater governmental subsidies in the past.
  
  2)If contemporary governments help to maintain and enrich the fine arts, private support for the arts will become necessary
  
  Even if contemporary governments help to maintain and enrich the fine arts, private support for the arts may not become necessary.
  
  3)in contemporary societies, aristocracies and religious institutions are not willing to help finance the fine ares
  
  In contemporary societies, aristocracies and religious institutions are willing to help finance the fine ares
  
  4)Serving as stewards of cultural heritage requires that contemporary societies help to maintain the fine arts.
  
  Serving as stewards of cultural heritage does not require that contemporary societies help to maintain the fine arts.
  
  5)Maintenance, advancement, and enrichment of the fine arts in any era require governmental subsidies.
  
  Maintenance, advancement, and enrichment of the fine arts in any era do not require governmental subsidies.
  
  I use what I like to call the "be a jerk and prove them wrong" method. When you're being stubborn and just want to prove someone wrong, all you do is take what they say, and tell them that the opposite is true. That's exactly what you're doing when you negate these types of sentences.
• Mr.lopez Member

  July 2016 172 karma

  I SERIOUSLY LOVE THIS COMMUNITY. THANK YOU EVERYONE FOR THE FEEDBACK
• 1 Like

  J.Y. Ping Administrator Instructor

  July 2016 14225 karma

  @cal6005 the relevant lessons that address / clarify what @quinnxzhang was trying to explain has been linked to in the reply.
  
  @quinnxzhang thanks for your reply, always helpful! I believe the lessons I linked to provide a complete answer. If you think the LSAT covers something that 7Sage does not, please do let me know. There are plenty of things that 7Sage doesn't cover, like modal logic for example. But I believe I've included everything in the course that you'll encounter on the LSAT.
• quinnxzhang Member

  July 2016 611 karma

  @"J.Y. Ping" I think 7sage does cover everything necessary for the LSAT -- (though I will say that knowing some basic modal logic would really help on 77.4.20). And I think the lessons you linked on quantifiers and their negations are good.
  
  However my objection has more to do with the way LSAT courses represent quantified sentences. The following two sentences are very different: (1) If Alan went to the park, then Beth went to the park. (2) All apes are big. However, both are represented the same way in LSAT courses, i.e. "A→B", and I think this representation leads to a lot of confusion.
  
  I don't want to derail this thread, but I'd be happy to start a new thread or PM you to discuss this in more detail.
• 1 Like

  J.Y. Ping Administrator Instructor

  July 2016 14225 karma

  @quinnxzhang I would love to hear your suggestions for improving the course! You have my email.
• 2 Likes

  quinnxzhang Member

  July 2016 611 karma

  @"J.Y. Ping" Sure thing, I sent a (rather long) email to your 7sage email! Let me know if you didn't get it for any reason.
• nye8870 Alum ⭐

  July 2016 1749 karma

  @blah170blah said:
  I would just advise keeping the nuance of "WONT NECESSARILY" in your mind
  

  Yes. Because the statement Dog sick --leads to--> seeming tired and lazy is negated by allowing instances of sick dogs not seeming tired and lazy. So the negation is actually Dog Sick --some-- don't seem tired and lazy.
• 1 Like

  cal6005 Free Trial Member

  July 2016 edited July 2016 106 karma

  @quinnxzhang said:
  To be precise, your sentence, "If a dog is sick, it will seem tired and lazy", actually expresses the following proposition: Every dog is such that if it's sick, it will seem tired and lazy. The negation of this is: Some dog is such that it's sick and will not seem tired and lazy. Why?
  

  @quinnxzhang said:
  Recall that not all is equivalent to some not.
  

  @quinnxzhang Thank you so much for explaining this in more detail!! I totally understand this explanation and understand why my method of negation is incorrect. I guess what works in my head isn't necessarily what I should share with others on here And now I can correct how I approach these questions in my own study. If you have any more basic logical concepts to share that you think are important, please share! I'd be interested in reading more of your explanations.

  @rachel said:
  When @quinnxzhang shows the negation using conditional diagrams, I believe he is simply showing that the negation of a conditional statement results in two conditions NO LONGER having a conditional relationship with each other. In other words, you can have one without the other. The negation of the dog statement using the ~(A > method that he showed means that you can have a sick dog and it will not necessarily be tired and lazy. You can have A without having B, whereas previously, if you had A, you necessarily had B.
  

  Also, thanks for this explanation, too @rachel! Definitely makes more sense to me now.
• Cant Get Right Yearly + Live Member Sage ⭐ 🍌 7Sage Tutor

  July 2016 27902 karma

  It looks like this question has been answered very well and thoroughly, but just thought I'd pitch in my buck o' 5.
  
  I think @stepharizona 's method is really simple and effective. You have to deny the relationship between the sufficient and necessary terms.
  
  So if you have A --> B, you get "it is not the case that A --> B." You're not saying that A is not the case, and you're not saying that B is not the case. You're saying that the --> is not the case. It is not true that A is sufficient for B. It is possible to have A and not B.
  
  For the purposes of the LSAT, I think this is the most concise way to think about it. When you really understand this method, it becomes easy to see how you can rephrase a statement more naturally. You don't really need to, but sometimes it's just a little easier to apply. So, you can turn
  
  "It is not the case that maintenance, advancement, and enrichment of the fine arts in any era require governmental subsidies," into "Maintenance, advancement, and enrichment of the fine arts in any era doesn't necessarily require governmental subsidies."
  
  A little easier to work with once you understand how to get there. Again, it's all about denying the relationship between the two terms. B is not necessary for A.