Statement Negation Drill

[Nadia0702]

Hi PS,
For #14 "Skating should be enjoyed not only by the young, but by the old as well."

My answer was: "Skating should be enjoyed neither by the young nor by the old."

The answer in the book was "Skating should not be enjoyed by both the young and the old."

I don't think my answer is equivalent to the right answer, as it appears that mine does not leave open the possibility of either group enjoying skating, yet the right answer does leave that possibility open. However, I am not sure why my answer is wrong. Thoughts?

Thanks!
Nadia

[Nikki Siclunov]

Hi Nadia,

Good question! Let's think about what is the essence of logical opposition: the binary you form needs to be completely exhaustive, i.e. it shouldn't leave a situation unaccounted for. So, the opposite of "Ana and Bob both go to the movies" would be "Ana and Bob do not both go to the movies." "Not both" could mean several different things: Ana goes without Bob, Bob goes without Ana, or neither of them goes. That way, the binary "both/not both" is exhaustive: there is no combination unaccounted for.

The same is true with your example. The initial proposition is that skating should be enjoyed by both the young and the old. The logical opposite to that claim would be that skating should not be enjoyed by both the young and the old: as long as at least one of the two groups does not enjoy skating, the logical opposite would take it into account. By comparison, your answer was the polar opposite of the initial proposition: skating should be enjoyed by neither group. But what about the situation where the young enjoy skating but the old don't (or vice versa)? That situation would not be taken into account either by the initial proposition (both should enjoy it), nor by your formulation of the logical opposite (neither should enjoy it). This is a problem, because the binary you just formed is not completely exhaustive of all possible outcomes (combinations). To avoid that situation, simply negate "both" by saying "not both": the latter includes the possibility of "neither," but also allows for all other possible outcomes except "both."

Hope this helps! Let me know

[Nadia0702]

Nikki,
This is an awesome explanation! Makes perfect sense now Thank you!

Nadia

[Toby]

Hello!

I have a question about statement negation in general. I am struggling to identify the scenarios in which I should hedge my language because I'm having hard time knowing when I should change the "absoluteness" of the verbs when I do the Opposition Construct. After doing Lesson 5's "Statement Negation Drill" on pages 5-36-37 and noticing that my answers did not match the absoluteness of the verbs of in the correct responses, I posted a question on the forum and got some helpful advice. After doing this drill, however, I seem to be having the same problem. The language that I used in my answers for this drill is often too weak in comparison to the language used in the correct answers. For example, I negated the statement in #10 to be

"Overall water pressure may not necessarily be the primary determinant of safety at public water processing facilities."

I chose to hedge the language in my answer because I thought that doing so would ensure that I created the logical opposite instead of the polar opposite. The correct answer for #10 is "Overall water pressure is not the primary determinant of safety at public water processing facilities." Similarly, I negated the statement in #11 to be

"At least some of the cafe's patrons may be aware that the cafe does not bake the doughnuts it sells."

Again, I hedged my language in this answer because I did want not to create a negated statement that was the polar opposite of the original sentence. The correct answer, however, maintains the absoluteness of the verbs in the original sentence by saying "Many of the cafe's patrons are unaware that the cafe does not bake the doughnuts it sells."

I suspect that the root of my problem is negating too many parts of the statement; when I change the strength of the language, I am essentially negating the statement twice. In other words, when I change the strength of the language, I am negating certain parts of the statement, but I may not necessarily be negating the correct aspects of the sentence. Therefore, I need help determining when altering the absoluteness of language is the right way to negate a sentence and when adding a "not" into the sentence is the correct way to logically negate the sentence. Is this hypothesis correct?

Put in a much simpler and shorter way, I would really appreciate more tips on how to determine when I should alter the strength of a statement's language in an Opposition Construct. Thank you so much for your help!

Toby

[Adam Tyson]

Much of the time, Toby, negation is as simple as inserting or deleting a "not" in the answer choice. The goal, however the statement is structured and whether or not a "not" is the best way to do it, negation is about making the answer choice false. I've coached students to try this approach when they are unsure about their negation: just insert at the beginning of the answer the phrase "it is not true that". For example, if you want to negate the claim that "for some consumers, marketing efforts aimed at bolstering confidence in the manufacturers of the advertised product, rather than in the products themselves, has the opposite effect", you could just say "it is not true that for some consumers, marketing efforts aimed at...".

While we do usually look for logical opposition - in my example, the logical opposite of "some" is "none", so a good negation would be "for no consumers do the marketing efforts aimed at..." - polar opposition isn't something to be afraid of. I often find it easier to use polar opposition when negating statements, and just as accurate and effective. So how do I negate "all dogs go to heaven"? Logically, I would say "not all dogs go to heaven", and I have done the job. If I used polar opposition, I would say "no dogs go to heaven", and that would also do the job. So why quibble over which one to use?

Typically, logical opposition is safer, because sometimes the polar opposite can occasionally mess things up. Not often, though, so do what comes naturally and don't force it. In your examples, you were just trying a little too hard, being a little too careful. Keep it simple, and don't be afraid of a negation that seems a little extreme. Most of the time it's going to work out just fine.

Good luck!

[Toby]

Thank you so much, Adam. Your advice really helped clarify statement negation for me.

[Blueballoon5%]

Hi! I have some questions about this drill.

1.) Is it possible to just remove the "not" in this sentence, rather than change "most" to "less than half"?

8.) I am a little confused with this sentence. When I approached this sentence, I first changed it to a conditional statement: "We will not lose our rights We protected our rights." Than I negated the necessary condition, making this statement: "We will not lose our rights We did not protect our rights." I translated this statement to a sentence form: "If we will not lose our rights, then we did not protect our rights." I don't understand where I went wrong, because this sentence doesn't really make sense. For example, how can we put a future tense in the sufficient condition?

The answer key on page 6-75 seems to use the term "even if" in the conditional statement. The sentence in the answer key reads, "Even if we protect our rights, we will lose them." According to the powerscore guide for "even if" term (https://blog.powerscore.com/lsat/how-to ... snt-matter), the modifying phrase after "even if" shows us things that are not required for losing our rights. In other words, the the protection of our rights is not a requirement in the loss of our rights. Perhaps even more clearly, this sentence means that we can lose our rights, whether or not we tried to protect them. This seems to make sense to me, and seems like the logical opposite of the sentence in the drill. However, I do not understand why the lesson book decided to pursue this path (of using "even if") for this particular sentence? Why didn't the book do what I originally did (to first make it a conditional statement, then negate the necessary condition, and then translate it into a sentence).

11.) Can we change "unaware" to "aware," rather than changing "many" to "few"?

[Adam Tyson]

In order, Blueballoon:.

1) In this instance, yes - if "most drivers are good drivers", that would disprove that the claim that most are NOT good drivers. That's the goal of negation. Don't do this on a "some" statement, though! "Some drivers are good drivers" does NOT negate the claim that "some drivers are not good drivers", because it's possible that both claims are true.

8) The negation of any conditional claim is done by showing that the necessary condition is not actually necessary, that the sufficient condition can happen "even if" the alleged necessary condition does not happen. We don't make a new necessary condition that is the opposite of the original one, but rather we just say that it is no longer necessary. In this case, and starting from your original translation of "We will not lose our rights We protected our rights", the negation would look like this:

"We will not lose our rights we may or may not have protected them - there's no way to be sure."

To put that another way, we might say "protecting our rights isn't necessary". Not that it IS necessary that we DID NOT protect them, as you diagrammed, but that protection is no longer a necessary condition when we do not lose our rights.

11) Nope, that would be making the same sort of error as I described in the case of "some" earlier in this post. "Many are aware" and "many are unaware" can both be true at the same time, so those claims do not negate each other! Many people read this forum and many do not; many people live in Europe and many do not; many cats have long hair and many do not, and so on. These are all possible simultaneously! "Many" is a relative claim, and it's almost impossible to put a number on it. It's more than one, certainly, but other than that we just can't tell. It's not like "most", where you know that it is more than half. In this case, the way to negate "many are unaware" is either to say "few are unaware" (because few is the opposite of many - you can't be both few and many at the same time) or else "not many are unaware."

Continue the good work! Good luck!