I was having trouble understanding that reasoning for the kingdoms in Westeros set up. Why is it that support of peace polcies, are required or the necessary conditions for kingdoms in Westeros?
In my math undergrad, I remember one of my teachers saying that definitions are indicate "if and only if." Does that mean there are biconditional indicators, as far as the LSAT is concerned?
For example, "The definition of an apple is a red fruit." Doesn't that mean that "A fruit is red if and only if it's an apple?"
If that is the definition of an apple. then that means all apples are red fruit.
So in lawgic, its: A--> RF.... the Contra would be /RF-->/A
You're confusing the necessary for the sufficient. Apples are essentially part of the red fruit group/superset. Just because its a red fruit doesn't mean its an apple (cherry, rasberry, watermelon cube. etc.), but if its an apple its a red fruit.
I think I understand the concept but on the last question I took Support as the sufficient indicator and secure peace as the necessary indicator. I think of sufficient as the "trigger" so i'm a bit confused on how to differentiate the sufficient indicator on this one.
I am so confused about what goes on which side of the arrow. Why can it not be memorization -> mastery? I always forget what is supposed to be on which side of the arrow. Is it condition -> result, or result -> condition?
@AudgePodge123! Hi Podge, I'm learning just like so you take this with a grain of salt - but from what I understand, the order goes in a "whats needed" to get there kind of order. So in this instance, to get to mastery, you need memorization, so the memorization would be the necessary condition, to be sufficient for mastery.
Another example of this could be something like: Getting a good LSAT score requires learning the foundationals. This would go in order of LSAT -> Foundationals, because the foundationals is whats needed first, before getting a good LSAT score.
This is how my brain has been understanding it so far, keep in mind I could be completely wrong, but hopefully this helps a bit.
The first element in Lawgic I want to introduce is this thing "→" which we will call "the arrow." The → establishes a conditional relationship between whatever sits on either side of it.
The → points from a sufficient condition (left side) to a necessary condition (right side). If those conditions just happen to be subsets and supersets well, then the arrow points from the subset to the superset.
For me, the video lesson helps more so than the written one; but, I pasted the written lesson above.
@mekhi I liked your explanation. I was totally on board with that example. But I was having trouble understanding that reasoning for the kingdoms in Westeros set up. Do you mind sharing your thoughts on that particular one?
For the last set of examples in the video, I think it's helpful to just visualize the rule that a plural subject has an implied "all" statement (sufficient indicator) in front of it. If a sentence says "dolphins eat food," that's that same thing as "all dolphins eat food."
I was struggling with this for a while but I think it finally clicked so I am leaving this here.
take the contrapositive if you are unsure. for example
-> The students who mastered logic saw improvements in their PrepTest scores.
my initial thought the first time was Improvements -> mastering test scores and I obviously got it wrong, so I looked up some examples on YouTube that helped
think of a red object if I were to write in lawgic:
color -> red, which would read as color is sufficient for red, now if I take the contrapositive /red->/color this idea can't be right, because if there's no red there is no color doesn't makes sense. it could be blue, orange, yellow, etc. now we do the opposite: red -> color, red is sufficient for color, take the contra positive: /color -> /red, if no color then it can't be red, now this makes more sense, right, because it's either there is color or not, there can be no substitutes.
now applying this to the example:
I took improvements -> mastering test scores took the contrapositive /mastering logic -> /improve, but this can't be true, because mastering logic can be substituted what if their test scores improved because of a tutor, maybe the teacher handed out extra credit, maybe covid 2027 came out and they could use chatgpt to answer everything idk all I know is that its not plausible to say just because this one thing did not happen does that mean that you did not improve.
now for the right answer:
mastering logic -> improvements
/improvements -> /mastering logic applying that same logic that I did for the wrong answer with the substitution could improvements have a substitute either than if they did or not? no of course not stagnant? not improved. decreased? not improve its either or, which means that improvements are required on mastering logic, but mastering logic isnt the ONLY thing to improve test score.
being a color is REQUIRED for a red object, but being a red object isnt the ONLY color for the object to be. I hope this helps someone!
@180-Energy Has everyone who has improved their test scores mastered logic? Not necessarily. They could have improved their reading comprehension or stress management, for instance. Mastering logic is just one of many methods that are sufficient to improve your score.
Flip it around to see the contrapositive: If you do not see improvement in your test scores, you must not have mastered logic.
But a lack of mastery of logic is not sufficient to infer that your score will not improve. Again, take the example of improving your reading comprehension or stress management. If you fail to master logic AND you improve either of those skills, then your score may increase. Failing to master logic is not sufficient to infer that your score will plateau or dip.
For me the circle diagrams are very helpful for this. Within the larger set of people who have improved their scores, there are smaller subsets--categories of people who took different methods to improve. One subset is mastering logic, but several others exist. Managing stress and improving your reading comprehension are two other subsets, but I'm sure you could think of several others.
@180-Energy Hi, I was having the same difficulties as you just now. Maybe this will help. See improvements -> master logic would be false because just seeing improvements doesn't mean you mastered logic. If you started at 0 points with your score, and improved by 5 points.. would landing at a final score of 5 out of say 100 points be enough to say you've mastered logic (even though your score has improved)? Mastery of logic is not a necessary result of a score improvement. Master logic -> see improvements makes sense because improvements could be on one of the reasons you mastered logic, so improvements would be a necessary thing to get the end result of mastering logic.
Example 1: “An engaging plot will guarantee a novel’s commercial success.”
“Engaging plot” (sufficient condition) & “novel’s commercial success” (necessary condition) → we know this because of the phrase [will guarantee].
Plot → Success
Example 2: “Mastering conditional logic requires some amount of memorizing conditional indicators.”
“Mastering conditional logic” (sufficient indicator) & “some amount of memorizing conditional indicators” (necessary condition) → we know this because of the phrase [requires].
Mastery → Memorization
Example 3: ‘The students who mastered logic saw improvements in their PrepTest scores.”
“Students who mastered logic” (sufficient indicator) & “improvements in their PrepTest scores” (necessary condition)
subject → predicate
Mastery → Improve
Example 4: “The kingdoms in Westeros whose economies rely predominantly on trade support foreign policies that aim to secure peace.”
“Kingdoms in Westeros whose economies rely predominantly on trade” (subject/sufficient condition) & “foreign policies that aim to secure peace.” (predicate/ necessary condition)
@Ikaarin I had to literally sound it out for myself to make that sentence make sense, but in doing so, I realized that it was a standalone subject that fit into a superset!
I don't really see how the Westeros example is a conditional statement. and does the subject --> predicate thing work on every example? or just those without indicators
Something that helps me (but is also not foolproof) is by trying to insert conditional indicators without changing the rest of the wording when applicable, such as "[all] students who mastered logic..." Rephrasing it altogether can also help but it's riskier.
i thought we were told that the idea immediately following the indicator is the necessary condition, so how is the second sentence still the same plot -> success and not success -> plot ?
Do sufficient and necessary conditions relate to using an active or passive voice? For instance the subject being acted upon, or if the subject receives the action.
@LexiSmith04 This is a good question. I'd say the answer is not really.
"Bananas are yellow."
"Yellow is the color of bananas."
These mean the same thing.
So if we choose to think of these as "banana --> yellow", that's not wrong.
(I think you might be asking this question since the second form seems susceptible to an interpretation "Yellow --> a color possessed by bananas".
I'll just say that that's not wrong, either, though probably not the most useful way to think about the statement. Often there are multiple ways to express the conditionality in a statement, each way focused on a different aspect of the relationship, but none of them technically incorrect. Which way is most useful to think about depends on the surrounding context.)
@KayleeMurray What's sort of helped me grasp the concept of sufficiency and necessity better is to treat sufficiency as the "if" or the "trigger" and necessity is the "then" or the result.
For example, "The students who mastered logic saw improvements in their PrepTest scores."
The result is improvement in their scores so that is the necessity.
Same with "The kingdoms in Westeros whose economies rely predominantly on trade support foreign policies that aim to secure peace."
I have a problem with continually mixing up my necessary and sufficient conditions - I think it stems from my urge to think of these sentences linearly - for example :
mastering conditional logic requires some amount of memorizing conditional indicators.
every bone in my body tells me that "mastering conditional logic" is the necessary condition, as it is a direct result of "memorizing conditional indicators" this can usually be tamed by translating to Lawgic using indicator words, but without the indicator words available, I need to restructure my thought process - does anyone have any tips on how to avoid thinking in these terms?
If the necessity does NOT happen, it guarantees the FAILURE of the sufficient.
If the sufficient has happened, then it must mean the necessity also happened.
So in your example:
mastering conditional logic requires some amount of memorizing conditional indicators
If we do not memorize some amount of the conditional indicators then we will certainly fail to master conditional logic.
If we mastered the conditional logic then that means we must have memorized conditional indicators.
We cannot be sure that just because we memorized conditional indicators that we mastered conditional logic because there are other factors we must also do to achieve that goal. Memorizing is one of many factors. And we cannot say that if we did not master the conditional logic then it must mean we did not memorize the indicators because we could have done that successfully but failed to do some of the other things required.
@ArcherHeeren The fundamental issue is that you're thinking about conditionality as if it's the same thing as causation or chronology. In the statement "If A, then B," it's very easy to think that A causes B to be true, or that A happens first, then B happens after.
But strictly speaking that's not what conditionality is about. Very often, conditionals happen to overlap with cause and chronology in a way that's intuitive. That's why many conditional are easy to understand and the issue you raise doesn't confuse you.
But sometimes, conditionals are presented in a way where the sufficient condition isn't the "cause" and doesn't happen "before" the necessary. As in the example you give -- mastering the lsat requires understanding conditional indicators.
I think the first step to avoiding the confusion you describe is to remember that conditionality isn't the same thing as "left side causes the right side" or "left side happens first and then right side happens next." Conditionality means "left side, if true, allows us to conclude that the right side is true".
Also, this is why the indicators are so helpful to identify. If we understand what the indicators mean, then over time, our intuition will catch up when we translate dozens upon dozens (perhaps even hundreds of statements) accurately.
@180-Energy Can I ask what you mean by "couldn't it also be"? Are you asking could this be true? Or are you asking whether that's what the statement is asserting?
"To master logic it is necessary to see improvements on your test score"
@AlvinB Exactly! that's what's been on my mind throughout these lessons. I'm glad that someone else is seeing that too.
We wouldn't have time in the exam to do all this logical analysis, so we need to find which clause sounds like an absolute fact statement (conclusion) and which clause supports that clause (premise). For example,
It will not rain unless Zeus is mad.
=If not Zeus is mad, it will not rain.
=If it rains, then Zuest must be mad.
/Z->/R
R->Z
It is being claimed that for it to rain something specific/absolute happens, which is, Zeus needs to be mad i.e. it is required that Zeus is mad.
When you put it through the "why, because" test for premise-conclusion, you'll see that:
Zeus must be mad, why?-> Conclusion(receiving support)/Necessary
Because it will rain.->Premise (throwing support)/Sufficient
@NathanielWright I do the same thing and it helps a lot! It's like when we learned about hypotheses in elementary school (at least where we did). They always had to be if...then statements, and this logic makes some sense to apply to LR!
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125 comments
I was having trouble understanding that reasoning for the kingdoms in Westeros set up. Why is it that support of peace polcies, are required or the necessary conditions for kingdoms in Westeros?
@JuliannaCalder "A is B."
That structure translates to "If A, then B". Basically we can think of "is B" as a fact that's true about things that are A.
"Kingdoms in Westeros support policies."
Kingdoms in Westeros --> support policies.
If a kingdom doesn't support those policies, then they aren't a kingdom in Westeros.
In my math undergrad, I remember one of my teachers saying that definitions are indicate "if and only if." Does that mean there are biconditional indicators, as far as the LSAT is concerned?
For example, "The definition of an apple is a red fruit." Doesn't that mean that "A fruit is red if and only if it's an apple?"
@WilRothman
If that is the definition of an apple. then that means all apples are red fruit.
So in lawgic, its: A--> RF.... the Contra would be /RF-->/A
You're confusing the necessary for the sufficient. Apples are essentially part of the red fruit group/superset. Just because its a red fruit doesn't mean its an apple (cherry, rasberry, watermelon cube. etc.), but if its an apple its a red fruit.
Think NY-->USA = /USA-->/NY
I think I understand the concept but on the last question I took Support as the sufficient indicator and secure peace as the necessary indicator. I think of sufficient as the "trigger" so i'm a bit confused on how to differentiate the sufficient indicator on this one.
I am so confused about what goes on which side of the arrow. Why can it not be memorization -> mastery? I always forget what is supposed to be on which side of the arrow. Is it condition -> result, or result -> condition?
@AudgePodge123! Hi Podge, I'm learning just like so you take this with a grain of salt - but from what I understand, the order goes in a "whats needed" to get there kind of order. So in this instance, to get to mastery, you need memorization, so the memorization would be the necessary condition, to be sufficient for mastery.
Another example of this could be something like: Getting a good LSAT score requires learning the foundationals. This would go in order of LSAT -> Foundationals, because the foundationals is whats needed first, before getting a good LSAT score.
This is how my brain has been understanding it so far, keep in mind I could be completely wrong, but hopefully this helps a bit.
@mekhi This is really helpful! Thank you :)
@everleez
It is always...
SUFFICIENT CONDITION --> NECESSARY CONDITION
[see "Lawgic the Language" Lesson]
For me, the video lesson helps more so than the written one; but, I pasted the written lesson above.
@mekhi Thank you! That helps out a lot!
@mekhi I liked your explanation. I was totally on board with that example. But I was having trouble understanding that reasoning for the kingdoms in Westeros set up. Do you mind sharing your thoughts on that particular one?
for mastery and some memorization, how does this logically make sense or translate to the drawn diagram?
For the last set of examples in the video, I think it's helpful to just visualize the rule that a plural subject has an implied "all" statement (sufficient indicator) in front of it. If a sentence says "dolphins eat food," that's that same thing as "all dolphins eat food."
I was struggling with this for a while but I think it finally clicked so I am leaving this here.
take the contrapositive if you are unsure. for example
-> The students who mastered logic saw improvements in their PrepTest scores.
my initial thought the first time was Improvements -> mastering test scores and I obviously got it wrong, so I looked up some examples on YouTube that helped
think of a red object if I were to write in lawgic:
color -> red, which would read as color is sufficient for red, now if I take the contrapositive /red->/color this idea can't be right, because if there's no red there is no color doesn't makes sense. it could be blue, orange, yellow, etc. now we do the opposite: red -> color, red is sufficient for color, take the contra positive: /color -> /red, if no color then it can't be red, now this makes more sense, right, because it's either there is color or not, there can be no substitutes.
now applying this to the example:
I took improvements -> mastering test scores took the contrapositive /mastering logic -> /improve, but this can't be true, because mastering logic can be substituted what if their test scores improved because of a tutor, maybe the teacher handed out extra credit, maybe covid 2027 came out and they could use chatgpt to answer everything idk all I know is that its not plausible to say just because this one thing did not happen does that mean that you did not improve.
now for the right answer:
mastering logic -> improvements
/improvements -> /mastering logic applying that same logic that I did for the wrong answer with the substitution could improvements have a substitute either than if they did or not? no of course not stagnant? not improved. decreased? not improve its either or, which means that improvements are required on mastering logic, but mastering logic isnt the ONLY thing to improve test score.
being a color is REQUIRED for a red object, but being a red object isnt the ONLY color for the object to be. I hope this helps someone!
I find this quite confusing. I still seem to be confusing sufficient and necessary:
eg. The students who mastered logic saw improvements in their PrepTest scores.
To master logic it is necessary to see improvements on your test score
Master logic -> See improvements
Couldn't it also be that in order to see improvements its necessary to master logic?
See improvements -> Master logic
---------------------------------------------------------
eg. An engaging plot will guarantee a novel's commercial success.
I see an engaging plot as necessary to guarantee commercial success.
success -> engaging plot
But the answer is the opposite.
---------------------------------------------------------
eg. Some amount of memorizing conditional indicators is required to master conditional logic.
In my mind, the memorization aspect is necessary to master conditional logic.
Master conditional logic -> Memorization
@180-Energy Has everyone who has improved their test scores mastered logic? Not necessarily. They could have improved their reading comprehension or stress management, for instance. Mastering logic is just one of many methods that are sufficient to improve your score.
Flip it around to see the contrapositive: If you do not see improvement in your test scores, you must not have mastered logic.
But a lack of mastery of logic is not sufficient to infer that your score will not improve. Again, take the example of improving your reading comprehension or stress management. If you fail to master logic AND you improve either of those skills, then your score may increase. Failing to master logic is not sufficient to infer that your score will plateau or dip.
For me the circle diagrams are very helpful for this. Within the larger set of people who have improved their scores, there are smaller subsets--categories of people who took different methods to improve. One subset is mastering logic, but several others exist. Managing stress and improving your reading comprehension are two other subsets, but I'm sure you could think of several others.
@180-Energy Hi, I was having the same difficulties as you just now. Maybe this will help. See improvements -> master logic would be false because just seeing improvements doesn't mean you mastered logic. If you started at 0 points with your score, and improved by 5 points.. would landing at a final score of 5 out of say 100 points be enough to say you've mastered logic (even though your score has improved)? Mastery of logic is not a necessary result of a score improvement. Master logic -> see improvements makes sense because improvements could be on one of the reasons you mastered logic, so improvements would be a necessary thing to get the end result of mastering logic.
I have notes:
Example 1: “An engaging plot will guarantee a novel’s commercial success.”
“Engaging plot” (sufficient condition) & “novel’s commercial success” (necessary condition) → we know this because of the phrase [will guarantee].
Plot → Success
Example 2: “Mastering conditional logic requires some amount of memorizing conditional indicators.”
“Mastering conditional logic” (sufficient indicator) & “some amount of memorizing conditional indicators” (necessary condition) → we know this because of the phrase [requires].
Mastery → Memorization
Example 3: ‘The students who mastered logic saw improvements in their PrepTest scores.”
“Students who mastered logic” (sufficient indicator) & “improvements in their PrepTest scores” (necessary condition)
subject → predicate
Mastery → Improve
Example 4: “The kingdoms in Westeros whose economies rely predominantly on trade support foreign policies that aim to secure peace.”
“Kingdoms in Westeros whose economies rely predominantly on trade” (subject/sufficient condition) & “foreign policies that aim to secure peace.” (predicate/ necessary condition)
Subject → Predicate
Trade → Peace
I literally read it as some "trade support foreign policies" instead of seeing support as the main verb lol
@Ikaarin I had to literally sound it out for myself to make that sentence make sense, but in doing so, I realized that it was a standalone subject that fit into a superset!
I don't really see how the Westeros example is a conditional statement. and does the subject --> predicate thing work on every example? or just those without indicators
@SarahHolmes754 If -> Then. If kingdoms rely on trade, then they will support policies
Something that helps me (but is also not foolproof) is by trying to insert conditional indicators without changing the rest of the wording when applicable, such as "[all] students who mastered logic..." Rephrasing it altogether can also help but it's riskier.
I thought the "Let's Review" part of the video was another example so I started finding the subject predicate of it 😂😭
this lesson was fun
i thought we were told that the idea immediately following the indicator is the necessary condition, so how is the second sentence still the same plot -> success and not success -> plot ?
Do sufficient and necessary conditions relate to using an active or passive voice? For instance the subject being acted upon, or if the subject receives the action.
@LexiSmith04 This is a good question. I'd say the answer is not really.
"Bananas are yellow."
"Yellow is the color of bananas."
These mean the same thing.
So if we choose to think of these as "banana --> yellow", that's not wrong.
(I think you might be asking this question since the second form seems susceptible to an interpretation "Yellow --> a color possessed by bananas".
I'll just say that that's not wrong, either, though probably not the most useful way to think about the statement. Often there are multiple ways to express the conditionality in a statement, each way focused on a different aspect of the relationship, but none of them technically incorrect. Which way is most useful to think about depends on the surrounding context.)
Hmmmm. Yeah, no. I'm taking my Webster's dictionary to the LSAT as part as my accomodation.
I have been having trouble grasping this concept, but this video has helped me tremendously.
@mibuch commenting for reference
@mibuch commenting for reference
brain mush
I am definitely getting confused in more complicated sufficient and necessary conditions.
Hopefully more practice equals more accuracy.
so does this mean in these basically the subject is the sufficient and the predicate is the necessary?? im lost
@KayleeMurray I'm confused on this too. It seems like this is what they are trying to say.
@KayleeMurray What's sort of helped me grasp the concept of sufficiency and necessity better is to treat sufficiency as the "if" or the "trigger" and necessity is the "then" or the result.
For example, "The students who mastered logic saw improvements in their PrepTest scores."
The result is improvement in their scores so that is the necessity.
Same with "The kingdoms in Westeros whose economies rely predominantly on trade support foreign policies that aim to secure peace."
The result is supporting foreign policy.
Hope this helps! :)
@MnM this was actually a great explanation, Thanks!!
@MnM this is awesome. thank you!
I have a problem with continually mixing up my necessary and sufficient conditions - I think it stems from my urge to think of these sentences linearly - for example :
mastering conditional logic requires some amount of memorizing conditional indicators.
every bone in my body tells me that "mastering conditional logic" is the necessary condition, as it is a direct result of "memorizing conditional indicators" this can usually be tamed by translating to Lawgic using indicator words, but without the indicator words available, I need to restructure my thought process - does anyone have any tips on how to avoid thinking in these terms?
@ArcherHeeren Try thinking like this:
If the necessity does NOT happen, it guarantees the FAILURE of the sufficient.
If the sufficient has happened, then it must mean the necessity also happened.
So in your example:
If we do not memorize some amount of the conditional indicators then we will certainly fail to master conditional logic.
If we mastered the conditional logic then that means we must have memorized conditional indicators.
We cannot be sure that just because we memorized conditional indicators that we mastered conditional logic because there are other factors we must also do to achieve that goal. Memorizing is one of many factors. And we cannot say that if we did not master the conditional logic then it must mean we did not memorize the indicators because we could have done that successfully but failed to do some of the other things required.
Therefore:
memorizing indicators = necessary
mastering = sufficient
Hope that is helpful!
@ArcherHeeren The fundamental issue is that you're thinking about conditionality as if it's the same thing as causation or chronology. In the statement "If A, then B," it's very easy to think that A causes B to be true, or that A happens first, then B happens after.
But strictly speaking that's not what conditionality is about. Very often, conditionals happen to overlap with cause and chronology in a way that's intuitive. That's why many conditional are easy to understand and the issue you raise doesn't confuse you.
But sometimes, conditionals are presented in a way where the sufficient condition isn't the "cause" and doesn't happen "before" the necessary. As in the example you give -- mastering the lsat requires understanding conditional indicators.
I think the first step to avoiding the confusion you describe is to remember that conditionality isn't the same thing as "left side causes the right side" or "left side happens first and then right side happens next." Conditionality means "left side, if true, allows us to conclude that the right side is true".
Also, this is why the indicators are so helpful to identify. If we understand what the indicators mean, then over time, our intuition will catch up when we translate dozens upon dozens (perhaps even hundreds of statements) accurately.
@Kevin_Lin I'm having a similar issue in which I see it both ways and get very confused which goes where. In the example:
eg. The students who mastered logic saw improvements in their PrepTest scores.
To master logic it is necessary to see improvements on your test score
Master logic -> See improvements
Couldn't it also be that in order to see improvements its necessary to master logic?
See improvements -> Master logic
@180-Energy Can I ask what you mean by "couldn't it also be"? Are you asking could this be true? Or are you asking whether that's what the statement is asserting?
"To master logic it is necessary to see improvements on your test score"
The question is what is that statement saying?
The subject -> predicate was a lightbulb moment. Thank you for explaining it that way!
@CheyenneBandy So does JY mean it is always Subject ---> Predicate? If so this is really cool. Also a lightbulb moment for me
Would you say a good idea is that the sufficient clause is the main point that is "doing" the work? While necessary receives the work?
@AlvinB Exactly! that's what's been on my mind throughout these lessons. I'm glad that someone else is seeing that too.
We wouldn't have time in the exam to do all this logical analysis, so we need to find which clause sounds like an absolute fact statement (conclusion) and which clause supports that clause (premise). For example,
It will not rain unless Zeus is mad.
=If not Zeus is mad, it will not rain.
=If it rains, then Zuest must be mad.
/Z->/R
R->Z
It is being claimed that for it to rain something specific/absolute happens, which is, Zeus needs to be mad i.e. it is required that Zeus is mad.
When you put it through the "why, because" test for premise-conclusion, you'll see that:
Zeus must be mad, why?-> Conclusion(receiving support)/Necessary
Because it will rain.->Premise (throwing support)/Sufficient
What's really helped me is forcing "if, then" to fit in the sentence. Not sure if this is a bad habit or not, but for example:
"The students who mastered logic saw improvements in their PrepTest scores."
What I did for this was intuitively divide up the sentence into the subject and predicate, then fit "If" and "Then" before them, resulting in:
"if you are a student who mastered logic, then you saw improvements to your PrepTest score"
It's really a backwards way of doing essentially the same thing described in this video, but I've found it to be much more intuitive for myself
@NathanielWright I do the same thing and it helps a lot! It's like when we learned about hypotheses in elementary school (at least where we did). They always had to be if...then statements, and this logic makes some sense to apply to LR!