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General questions relating to LSAT Logical Reasoning.
 lsatjourneygirl
  • Posts: 22
  • Joined: May 03, 2016
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#23892
Hello,

I realize negating answer choices for Assumption questions is not the go to move, but at times, I need it for the final two answer choices. However, I am not sure how to properly negate certain answer choices:

For example

1. Cats sometimes scratch when it is reasonable to cuddle instead.

2. There are cats who never purr but who often scratch.

These are modified versions of answer choices that often confuse me when it comes to negations.

Thank you for your help!
 Nikki Siclunov
PowerScore Staff
  • PowerScore Staff
  • Posts: 1365
  • Joined: Aug 02, 2011
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#23898
Hi lsatjourneygirl,

Negating a statement consists of creating the logical opposite of that statement, i.e. a statement that denies the truth of the original. This is often a relatively simple task, which usually requires the mere insertion or removal of the word “not,” but it takes a bit more effort when the sentence you need to negate has a more complicated structure.

Negating Compound Statements

A compound statement refers to a statement made up of two independent clauses. How you negate the meaning of such statements depends on whether the independent clauses are connected to one another using a conjunction (and; both... and; neither...nor; not only... but also; as well as) or a disjunction (or; either...or).

Negating Conjunctions

To negate a conjunction such as I love you and you love me requires showing that the two clauses cannot be both true: it is simply not the case that we both love each other. In effect, this would mean one of three things:
  • I don’t love you, or
  • You don’t love me, or
  • Neither of us loves the other.
Thus, whenever you negate a compound sentence in which the conjunction (and) or any of its synonyms are used, negate the main verb and then change the conjunction (and) into a disjunction (or):
  • AND :arrow: OR
For example:
  • I want both glory and fame :arrow: I don't want glory or I don't want fame (or I don't want either);
  • We can neither win nor surrender :arrow: We can either win or surrender;
  • Ike is not only brave, but is also smart :arrow: Ike is not brave or not smart (or is neither brave nor smart
Negating Disjunctions

To negate a disjunction such as Jon is either a doctor or a lawyer requires showing that Jon is neither a doctor nor a lawyer. In effect, this would mean the following:
  • Jon is not a doctor, and
  • Jon is not a lawyer
Whenever you negate a compound statement in which a disjunction (or) is used, negate the main verb and then change the disjunction (or) into a conjunction (and):
  • OR :arrow: AND
For example:
  • I will adopt a dog or a cat :arrow: I will adopt neither a dog nor a cat (i.e. I will not adopt a dog and I will not adopt a cat)
Negating Complex Statements

The examples you provide below are complex sentences, i.e. sentences that contain one independent clause and at least one dependent clause. Some definitions are in order:
  • An independent clause is a group of words that contains a subject and a verb, expresses a complete thought, and can stand alone as a sentence.
  • A dependent clause is a group of words that contains a subject and a verb, does not express a complete thought, and cannot stand alone as a sentence.
When logically negating complex sentences, always negate the verb in the independent (i.e. main) clause only. The dependent clause does not bear the weight of the negation, and should be left intact.

Keep in mind, however, that the logical opposite may require modifying the dependent clause, as shown below, in order to maintain the logical cohesion of the negated statement. Independent clauses are underlined.
  • Though he was rich, he was unhappy :arrow: He was happy, regardless of whether he was rich.
  • Wherever you go, you can always find beauty :arrow: You cannot find beauty wherever you go.
  • The play was fascinating, as we expected :arrow: The play was not fascinating, contrary to expectations.
Negating Beliefs and Opinions in Noun Clauses

When test makers introduce views or opinions, they typically do so by using a dependent clause called a noun clause. A noun clause is simply two or more words that act like a noun. It can be the object of a verb (“I believe that stealing is immoral”) or it can complement an adjective (“It was wrong of him to steal”). All noun clauses are dependent clauses. Consequently, the noun clause in a statement expressing a belief or an opinion should not bear the weight of the negation. For example, the logical opposite of I believe that stealing is immoral is I do not believe that stealing is immoral.

That said, it is always critical to understand the implications of your oppositional construct, and simplify the resulting statement whenever possible. Sometimes, this may require manipulating the noun clause. For instance, the statement I do not believe that stealing is immoral contains a double negative, which translates to I believe that stealing is moral. Be wary of double or triple conceptual negatives, in which one negative concept cancels out another negative concept, which cancels out the original.

Negating Causality

The proper negation of a complex causal statement requires showing that the cause does not necessarily produce the effect. Keep in mind, however, that the logical opposite of the causal statement may also require modifying the dependent clause in order to maintain the logical cohesion of the negated statement. See examples below. Independent clauses are underlined.
  • Apple’s stock price went up because of their Q4 report :arrow: Apple’s stock price did not go up because of their Q4 report.
  • Because hormone levels are correlated with heart disease, they influence heart disease :arrow: Hormone levels do not influence heart disease, even though they are correlated with heart disease.
Negating Conditionality

The proper negation of a conditional statement requires showing that the sufficient condition can occur even if the necessary condition does not occur, i.e. that the necessary condition is not, in fact, necessary.

The logical opposite of All that glitters is gold is simply Not all that glitters is gold (i.e. some things may glitter even if they are not gold).

For example:
  • You must study in order to succeed :arrow: You need not study in order to succeed (i.e. if may succeed even if you don't study)
  • Only the brave die young :arrow: Those who are brave are not the only ones who die young (i.e. you can die young even if you are a coward)
  • Unless the package is sent by air, it will not arrive tomorrow :arrow: The package may arrive tomorrow, even if it is not sent by air.
Quite often, the logical opposite of a conditional statement is formed using the phrase even if. Note that even if is not, by itself, an indicator of a sufficient condition: it merely states that the absence of one condition does not preclude the other from occurring.

Negating Complex-Compound Statements

Some complex sentences will contain multiple dependent clauses, whereas others contain multiple independent clauses. Similarly, some conditional statements will join multiple sufficient and/or necessary conditions. When negating such statements, focus on negating the independent (main) clause! Whenever the clauses (or conditions) are joined with a conjunction and or a disjunction or, use the rules of compound statement negation and negate the conjunction into a disjunction, and vice versa.

For example:
  • To comply with the doctor’s orders, patients must drink either tea or coffee, but not both

    ..... ..... NEGATES TO:

    Some participants drank neither tea nor coffee, and some drank both.

    -----------
  • Equipping a car with both power windows and power locks is not significantly more difficult than equipping it with only power locks.

    ..... ..... NEGATES TO:

    Equipping a car with both power windows and power locks is significantly more difficult than equipping it with only power locks. (Note: The conjunction both remains intact in the negation, because the sentence uses a subordinating conjunction more…then, suggesting a comparative claim. Accordingly, the logical opposite would require negating the main, comparative claim, while preserving the dependent clause(s) intact.
Now, let's take a look at the examples you provided:
  • Cats sometimes scratch when it is reasonable to cuddle instead.

    ..... ..... NEGATES TO:

    Cats never scratch when it's reasonable to cuddle instead.

    The main (independent) clause is "cats sometimes scratch." Sometimes negates to never. The remainder remains intact.

    ------------
  • There are cats who never purr but who often scratch.

    ..... ..... NEGATES TO:

    Every cat that scratches also purrs (i.e., there are no cats that scratch without purring). Your original example shows that two propositions do not overlap, as we can have cats who scratch but never purr (Scratch, Purr). The logical opposite of this statement would deny the truth of the original, which requires showing that purring is a necessary condition for scratching: if every cat that scratches also purrs, that would be in direct contradiction of your original statement.
Here's a little homework for you: write down the logical opposite of each sentence below. I'll check them out and give you feedback :-)
  • No college can survive without the generosity of its alumni.
  • Mary was anxious to commence her studies.
  • Sugar consumption exacerbates the symptoms of ADHD.
  • Prescription warnings cannot benefit patients unless patients actually read them.
  • We must both shape public opinion and be adept at reacting to it.
  • Vegetarians are less likely to develop arthritis than are non-vegetarians.
  • Now that sedentary lifestyle is the norm, childhood obesity can be expected to increase.
  • It is not irrational to refuse to give to a worthy charity simply because one does not feel like doing so.
  • The car is equipped with both power windows and a sunroof.
  • Coffee drinkers are no more likely to exercise and eat healthily than are tea drinkers.
  • Proper nutrition has no health benefits that are as valuable as the boost that sleep purportedly gives to the body’s immune system.
  • An action harms those who perform it only if it also eventually harms others.
  • Farm animals either forage for themselves or feed on animal fodder.
  • We need to either increase taxes or demand higher wages.
  • The cities whose population declines have been attributed by experts to unemployment are not known to be among those cities whose population has been affected by lower birth rates.
  • Only those who are both romantic and cautious can truly fall in love.
  • You are not a realist unless you either believe in miracles or in yourself.
  • You are neither a realist nor a humanist if you believe in miracles.
  • It is rational not to believe in miracles, unless you are either romantic or idealistic.
  • Whereas many viewed the defendant’s plea for mercy as opportunistic, some were convinced that the police had failed to comply with their respective obligations.
  • The variations in longevity within a country that result from uneven access to healthcare are not always as large as the declines in longevity that scientists have attributed to poor nutrition.
  • There is little merit to claim that it is absurd to disapprove of those who reject popularly held beliefs merely because such beliefs are more likely to be false than true.
I realize this is a bit more than you bargained for, but logical negation is such a critical aspect of our approach to Assumption questions that it deserves investing some time into it.

Good luck! :-)
 lsatjourneygirl
  • Posts: 22
  • Joined: May 03, 2016
|
#24001
Thank you! I will get to those soon!
 lsatjourneygirl
  • Posts: 22
  • Joined: May 03, 2016
|
#25623
Nikki Siclunov wrote:Hi lsatjourneygirl,

Negating a statement consists of creating the logical opposite of that statement, i.e. a statement that denies the truth of the original. This is often a relatively simple task, which usually requires the mere insertion or removal of the word “not,” but it takes a bit more effort when the sentence you need to negate has a more complicated structure.

Negating Compound Statements

A compound statement refers to a statement made up of two independent clauses. How you negate the meaning of such statements depends on whether the independent clauses are connected to one another using a conjunction (and; both... and; neither...nor; not only... but also; as well as) or a disjunction (or; either...or).

Negating Conjunctions

To negate a conjunction such as I love you and you love me requires showing that the two clauses cannot be both true: it is simply not the case that we both love each other. In effect, this would mean one of three things:
  • I don’t love you, or
  • You don’t love me, or
  • Neither of us loves the other.
Thus, whenever you negate a compound sentence in which the conjunction (and) or any of its synonyms are used, negate the main verb and then change the conjunction (and) into a disjunction (or):
  • AND :arrow: OR
For example:
  • I want both glory and fame :arrow: I don't want glory or I don't want fame (or I don't want either);
  • We can neither win nor surrender :arrow: We can either win or surrender;
  • Ike is not only brave, but is also smart :arrow: Ike is not brave or not smart (or is neither brave nor smart
Negating Disjunctions

To negate a disjunction such as Jon is either a doctor or a lawyer requires showing that Jon is neither a doctor nor a lawyer. In effect, this would mean the following:
  • Jon is not a doctor, and
  • Jon is not a lawyer
Whenever you negate a compound statement in which a disjunction (or) is used, negate the main verb and then change the disjunction (or) into a conjunction (and):
  • OR :arrow: AND
For example:
  • I will adopt a dog or a cat :arrow: I will adopt neither a dog nor a cat (i.e. I will not adopt a dog and I will not adopt a cat)
Negating Complex Statements

The examples you provide below are complex sentences, i.e. sentences that contain one independent clause and at least one dependent clause. Some definitions are in order:
  • An independent clause is a group of words that contains a subject and a verb, expresses a complete thought, and can stand alone as a sentence.
  • A dependent clause is a group of words that contains a subject and a verb, does not express a complete thought, and cannot stand alone as a sentence.
When logically negating complex sentences, always negate the verb in the independent (i.e. main) clause only. The dependent clause does not bear the weight of the negation, and should be left intact.

Keep in mind, however, that the logical opposite may require modifying the dependent clause, as shown below, in order to maintain the logical cohesion of the negated statement. Independent clauses are underlined.
  • Though he was rich, he was unhappy :arrow: He was happy, regardless of whether he was rich.
  • Wherever you go, you can always find beauty :arrow: You cannot find beauty wherever you go.
  • The play was fascinating, as we expected :arrow: The play was not fascinating, contrary to expectations.
Negating Beliefs and Opinions in Noun Clauses

When test makers introduce views or opinions, they typically do so by using a dependent clause called a noun clause. A noun clause is simply two or more words that act like a noun. It can be the object of a verb (“I believe that stealing is immoral”) or it can complement an adjective (“It was wrong of him to steal”). All noun clauses are dependent clauses. Consequently, the noun clause in a statement expressing a belief or an opinion should not bear the weight of the negation. For example, the logical opposite of I believe that stealing is immoral is I do not believe that stealing is immoral.

That said, it is always critical to understand the implications of your oppositional construct, and simplify the resulting statement whenever possible. Sometimes, this may require manipulating the noun clause. For instance, the statement I do not believe that stealing is immoral contains a double negative, which translates to I believe that stealing is moral. Be wary of double or triple conceptual negatives, in which one negative concept cancels out another negative concept, which cancels out the original.

Negating Causality

The proper negation of a complex causal statement requires showing that the cause does not necessarily produce the effect. Keep in mind, however, that the logical opposite of the causal statement may also require modifying the dependent clause in order to maintain the logical cohesion of the negated statement. See examples below. Independent clauses are underlined.
  • Apple’s stock price went up because of their Q4 report :arrow: Apple’s stock price did not go up because of their Q4 report.
  • Because hormone levels are correlated with heart disease, they influence heart disease :arrow: Hormone levels do not influence heart disease, even though they are correlated with heart disease.
Negating Conditionality

The proper negation of a conditional statement requires showing that the sufficient condition can occur even if the necessary condition does not occur, i.e. that the necessary condition is not, in fact, necessary.

The logical opposite of All that glitters is gold is simply Not all that glitters is gold (i.e. some things may glitter even if they are not gold).

For example:
  • You must study in order to succeed :arrow: You need not study in order to succeed (i.e. if may succeed even if you don't study)
  • Only the brave die young :arrow: Those who are brave are not the only ones who die young (i.e. you can die young even if you are a coward)
  • Unless the package is sent by air, it will not arrive tomorrow :arrow: The package may arrive tomorrow, even if it is not sent by air.
Quite often, the logical opposite of a conditional statement is formed using the phrase even if. Note that even if is not, by itself, an indicator of a sufficient condition: it merely states that the absence of one condition does not preclude the other from occurring.

Negating Complex-Compound Statements

Some complex sentences will contain multiple dependent clauses, whereas others contain multiple independent clauses. Similarly, some conditional statements will join multiple sufficient and/or necessary conditions. When negating such statements, focus on negating the independent (main) clause! Whenever the clauses (or conditions) are joined with a conjunction and or a disjunction or, use the rules of compound statement negation and negate the conjunction into a disjunction, and vice versa.

For example:
  • To comply with the doctor’s orders, patients must drink either tea or coffee, but not both

    ..... ..... NEGATES TO:

    Some participants drank neither tea nor coffee, and some drank both.

    -----------
  • Equipping a car with both power windows and power locks is not significantly more difficult than equipping it with only power locks.

    ..... ..... NEGATES TO:

    Equipping a car with both power windows and power locks is significantly more difficult than equipping it with only power locks. (Note: The conjunction both remains intact in the negation, because the sentence uses a subordinating conjunction more…then, suggesting a comparative claim. Accordingly, the logical opposite would require negating the main, comparative claim, while preserving the dependent clause(s) intact.
Now, let's take a look at the examples you provided:
  • Cats sometimes scratch when it is reasonable to cuddle instead.

    ..... ..... NEGATES TO:

    Cats never scratch when it's reasonable to cuddle instead.

    The main (independent) clause is "cats sometimes scratch." Sometimes negates to never. The remainder remains intact.

    ------------
  • There are cats who never purr but who often scratch.

    ..... ..... NEGATES TO:

    Every cat that scratches also purrs (i.e., there are no cats that scratch without purring). Your original example shows that two propositions do not overlap, as we can have cats who scratch but never purr (Scratch, Purr). The logical opposite of this statement would deny the truth of the original, which requires showing that purring is a necessary condition for scratching: if every cat that scratches also purrs, that would be in direct contradiction of your original statement.
Here's a little homework for you: write down the logical opposite of each sentence below. I'll check them out and give you feedback :-)
  • No college can survive without the generosity of its alumni.
  • Mary was anxious to commence her studies.
  • Sugar consumption exacerbates the symptoms of ADHD.
  • Prescription warnings cannot benefit patients unless patients actually read them.
  • We must both shape public opinion and be adept at reacting to it.
  • Vegetarians are less likely to develop arthritis than are non-vegetarians.
  • Now that sedentary lifestyle is the norm, childhood obesity can be expected to increase.
  • It is not irrational to refuse to give to a worthy charity simply because one does not feel like doing so.
  • The car is equipped with both power windows and a sunroof.
  • Coffee drinkers are no more likely to exercise and eat healthily than are tea drinkers.
  • Proper nutrition has no health benefits that are as valuable as the boost that sleep purportedly gives to the body’s immune system.
  • An action harms those who perform it only if it also eventually harms others.
  • Farm animals either forage for themselves or feed on animal fodder.
  • We need to either increase taxes or demand higher wages.
  • The cities whose population declines have been attributed by experts to unemployment are not known to be among those cities whose population has been affected by lower birth rates.
  • Only those who are both romantic and cautious can truly fall in love.
  • You are not a realist unless you either believe in miracles or in yourself.
  • You are neither a realist nor a humanist if you believe in miracles.
  • It is rational not to believe in miracles, unless you are either romantic or idealistic.
  • Whereas many viewed the defendant’s plea for mercy as opportunistic, some were convinced that the police had failed to comply with their respective obligations.
  • The variations in longevity within a country that result from uneven access to healthcare are not always as large as the declines in longevity that scientists have attributed to poor nutrition.
  • There is little merit to claim that it is absurd to disapprove of those who reject popularly held beliefs merely because such beliefs are more likely to be false than true.
I realize this is a bit more than you bargained for, but logical negation is such a critical aspect of our approach to Assumption questions that it deserves investing some time into it.

Good luck! :-)

1. CS -> ~GA
2. Mary was not anxious to commence...
3. Sugar consumption does not...
4. Benefit -> ~Read
5. We do not have to shape public opinion or be adept at...
6. Vegetarians are more or at least as likely to...
7. ..., childhood obesity cannot be expected to increase
8. It is irrational to...
9. The car is not equipped with power windows or sunroof
10. Coffee drinkers are less or at least as likely to...
11. Proper nutrition has health benefits that are as valuable...
12. There are other ways to harm others who perform an action aside from if it harms others.
13. Farm animals do not forage and feed on animal fodder.
14. We need to not increase taxes and demand higher wages.
15. The cities whose population declines have been attributed by experts to unemployment ARE known to be...
16. There are people aside from those who are both romantic and cautious that can fall in love
17. R ---> don't believe in miracles and yourself
18. believe in miracles ----> you are either a realist or a humanist
19. it is rational to believe in miracles ---> not romantic and idealistic
20. ...., nobody was convinced...
21. ...... are always as large as the declines...
22. Because...., there is merit to claim that it is absurd to disapprove...
 Nikki Siclunov
PowerScore Staff
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  • Posts: 1365
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#25654
Hi lsatjourneygirl,

Thanks for taking the time to work on these oppositions. Unfortunately, your responses do not quite accomplish the task at hand!

The purpose of the drill is to train you to negate complex statements, which requires you to write the complete logical negation of each statement. Answering each prompt partially is not sufficient. For instance, let's take the first prompt ("No college can survive without the generosity of its alumni"). The original conditional diagram is:
  • College Survive :arrow: Generous Alumni
To logically negate this statement, you need to show that some colleges can survive even without the generosity of their alumni. In other words, the logical opposite requires showing that the sufficient condition can occur even in the absence of the necessary condition. By contrast, your response (CS -> ~GA) suggests that the survival of colleges requires lack of generosity, which is clearly incorrect. To avoid such confusion, please complete the drill articulating the logical oppositions in full form.

Thanks!
 lsatjourneygirl
  • Posts: 22
  • Joined: May 03, 2016
|
#25662
Some colleges can survive without the generosity of its alumni.
Mary was not anxious to commence her studies.
Sugar consumption does not exacerbates the symptoms of ADHD.
Prescription warnings can benefit patients, even without patients actually reading them.
We do not have to shape public opinion or be adept at reacting to it.
Vegetarians are as at least/more likely to develop arthritis than are non-vegetarians.
Now that sedentary lifestyle is the norm, childhood obesity cannot be expected to increase.
It is irrational to refuse to give to a worthy charity simply because one does not feel like doing so.
The car is equipped with both power windows and a sunroof.
Coffee drinkers are no more likely to exercise and eat healthily than are tea drinkers.
Proper nutrition has health benefits that are as valuable as the boost that sleep purportedly gives to the body’s immune system.
There are other ways to harm others who perform an action aside from if it it harms others.
Farm animals do not forage and feed on animal fodder.
We need not increase taxes and demand higher wages.
The cities whose population declines have been attributed by experts to unemployment are known to be among those cities whose population has been affected by lower birth rates.
Even if you are not those both romantic and cautious, you can truly fall in love.
You may not be a realist, even if you do not believe in miracles and in yourself.
You may/could be a realist or a humanist if you believe in miracles.
It is rational not to believe in miracles, even if you are either romantic or idealistic.
Whereas many viewed the defendant’s plea for mercy as opportunistic, nobody was were convinced that the police had failed to comply with their respective obligations.
The variations in longevity within a country that result from uneven access to healthcare are always as large as the declines in longevity that scientists have attributed to poor nutrition.
There is merit to claim that it is absurd to disapprove of those who reject popularly held beliefs merely because such beliefs are more likely to be false than true.
 lsatjourneygirl
  • Posts: 22
  • Joined: May 03, 2016
|
#25742
Hello!

I re-did the exercise, let me know if this is better, thank you for your help!
Nikki Siclunov wrote:Hi lsatjourneygirl,

Thanks for taking the time to work on these oppositions. Unfortunately, your responses do not adequately accomplish the task at hand.

The purpose of the drill is to train you to negate complex statements, which requires you to write the complete logical negation of each statement. Answering each prompt partially is not sufficient. For instance, let's take the first prompt ("No college can survive without the generosity of its alumni"). The original conditional diagram is:
  • College Survive :arrow: Generous Alumni
To logically negate this statement, you need to show that some colleges can survive even without the generosity of their alumni. In other words, the logical opposite requires showing that the sufficient condition can occur even in the absence of the necessary condition. By contrast, your response (CS -> ~GA) suggests that the survival of colleges requires lack of generosity, which is clearly incorrect. To avoid such confusion, please complete the drill articulating the logical oppositions in full form.

Thanks!
 Nikki Siclunov
PowerScore Staff
  • PowerScore Staff
  • Posts: 1365
  • Joined: Aug 02, 2011
|
#25868
Some colleges can survive without the generosity of its alumni.
Correct.
Mary was not anxious to commence her studies.
Correct.
Sugar consumption does not exacerbates the symptoms of ADHD.
Correct.
Prescription warnings can benefit patients, even without patients actually reading them.
Correct.
We do not have to shape public opinion or be adept at reacting to it.
Correct.
Vegetarians are as at least/more likely to develop arthritis than are non-vegetarians.
Correct. In other words, vegetarians are just as likely as non-vegetarians to develop arthritis.
Now that sedentary lifestyle is the norm, childhood obesity cannot be expected to increase.
Correct.
It is irrational to refuse to give to a worthy charity simply because one does not feel like doing so.
Make sure your negation makes sense to you: in other words, it’s OK to give to a worthy charity simply because you feel like it.
The car is equipped with both power windows and a sunroof.
Incorrect. The car is NOT equipped with both power windows and a sunroof.
(i.e. the car either has no power windows, or no sunroof, or it has neither)
Coffee drinkers are no more likely to exercise and eat healthily than are tea drinkers.
Incorrect. Coffee drinkers are more likely to exercise and eat healthily than are tea drinkers.
Proper nutrition has health benefits that are as valuable as the boost that sleep purportedly gives to the body’s immune system.
Correct.
There are other ways to harm others who perform an action aside from if it it harms others.
Syntax. Better said: We can harm ourselves even if we don’t harm others in the process.
Farm animals do not forage and feed on animal fodder.
Better said: Farm animals neither forage nor feed on fodder.
We need not increase taxes and demand higher wages.
Incorrect. We need not increase taxes OR demand higher wages (we don’t have to do either of these things).
The cities whose population declines have been attributed by experts to unemployment are known to be among those cities whose population has been affected by lower birth rates.
Correct.
Even if you are not those both romantic and cautious, you can truly fall in love.
Correct. You don't have to be both of these things to fall in love: you can be romantic but not cautious, or cautious and not romantic, or neither romantic nor cautious, and still fall in love :)
You may not be a realist, even if you do not believe in miracles and in yourself.
Incorrect. You can be a realist even if you do not believe in miracles or in yourself.
You may/could be a realist or a humanist if you believe in miracles.
Correct.
It is rational not to believe in miracles, even if you are either romantic or idealistic.
Incorrect. Believing in miracles is rational even if you are neither romantic nor idealistic.
Whereas many viewed the defendant’s plea for mercy as opportunistic, nobody was were convinced that the police had failed to comply with their respective obligations.
Correct.
The variations in longevity within a country that result from uneven access to healthcare are always as large as the declines in longevity that scientists have attributed to poor nutrition.
Correct.
There is merit to claim that it is absurd to disapprove of those who reject popularly held beliefs merely because such beliefs are more likely to be false than true.
Correct. But do you really know what this means? Simplify it:

It's OK to reject popular beliefs on the grounds that such beliefs are more likely to be false than true.

Good job!! This was an exceptionally tough drill :-)
 jessicamorehead
  • Posts: 84
  • Joined: Jul 07, 2017
|
#43965
HELP!! I'm confused with negating even simple ideas. For example, on page 5-36 "Humans need three gallons of water a day in order to survive." Would I just add a "not" and it would be negated? So, "Humans do NOT need three gallons of water a day in order to survive." However, the correct answer listed in the book says, " Humans do NOT NECESSARILY need three gallons of water a day in order to survive." Is that "necessarily" necessary or is my way correct as well?

Also, why would you need to say "may?" For example, "Purchasing a ticket is the only way to get inside." I negated it as "Purchasing a ticket is NOT the only way to get inside." However, the book says the correct answer is "Purchasing a ticket MAY NOT be the only way to get inside."
 Emily Haney-Caron
PowerScore Staff
  • PowerScore Staff
  • Posts: 577
  • Joined: Jan 12, 2012
|
#43972
Hi Jessica!

Great question. Remember that a logical opposite is different than a polar opposite. The polar opposite of the statement "a thing is true" is "a thing is not true." But the logical opposite would be "a thing is not necessarily true." Often, we shorten this to just adding in not, and most of the time that'll be sufficient to get you to the right answer choice! Generally, though, I'd recommend getting in the habit of remembering that the logical opposite of a statement that something must happen will be that something doesn't HAVE to happen, not that something WON'T happen. Do you see how those are different? Your way isn't wrong, but it is less precise, if that makes sense.

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