The thing that helped me was thinking of the if and then as metrics in which to measure something. One is a measurement of time past 5 minutes. The other is a measurement of being late.
Since the measurement of time past 5 minutes is on the right then you are not measuring for that metric. (17 minutes is irrelevant in the 2nd premise)
Since the measurement of being late is on the left, then you are measuring for that metric.
Nothing was mentioned about whether or not he was late in the 2nd premise, just that he arrived 17 minutes after the bell, so no valid conclusion can be drawn because the sentence ha.
Likely Mistake Made: You tried to measure for the 5+ minutes metric but its on the right, you only measure for the metric on the left (late or not). You assumed that being late was equivalent to 5+ minutes but they are separate.
So, necessary is the big bubble that catches all the conditions. So, by that logic, I feel like using "only if" turns the sufficient condition into a necessary condition. And both bubbles should be equivalent in size and trigger each other.
So like... if Elias arrived 17 minutes after the last bell, but he had a doctor's note or something. Some OTHER instance or possibility could be true in which he is arriving 5 minutes past the last bell but would not be considered late. In visual terms, he could be within the larger circle (more than 5 minutes after the bell), while not being in the smaller circle (cited as late).
@AidanW yeah this is my thought process too, I think its right. I am sorta visualizing the circles in my head as I read these to try and understand them.
The video explanation didn't specify that Kumar was a student so I thought the argument wasn't valid because it had an assumption that Kumar was a student...somehow reached the right answer in another way!
My brain hurt while trying to understand Kumar's case.
Anyways, what I understood from this lesson and from explanation in the comment section mostly (thanks to people clarifying it!), "only if" has exceptions. Kumar being late does not automatically put him in the subset of " cited as late". He could be. Or, he could not be cited as late; for example, he informed the school in advance about his medical appointment and arriving late, so the teacher would not put him as late. But the argument is silent in that regard.
Below is a basic example that helped me better understand Kumar's case:
It is a cat only if it is an animal.
We can NOT say:
If it is an animal, it is a cat.
Could be any animal e.g. dog, bird...
Being an animal is a necessity, but it is not sufficient for being a cat.
So even if Kumar arrived only six minutes after the bell, it would still be invalid to assume he would be marked late because he satisfies the necessary condition but not necessarily the sufficient condition?
@MilagrosZepeda I think it says that the only way he is guaranteed to be marked late is if he is more than five minutes past the last ring of the homeroom bell. Being 17 minutes after the last ring of the homeroom bell is different and doesn't trigger the conditional. It's really confusing because 17 minutes late is more than 5 minutes late, and you'd think it falls into that category. So what I learned is that if the argument contains "only if," then the conditional can only be triggered by saying the sufficient condition is happening in exactly the same way it was already stated in the argument. If it's not a word for word match, then it's probably the LSAT trying to trick you.
@BillyM_ So if the second premise listed said something along the lines of, "Kumar arrived 17 minutes after the last ring of the homeroom bell and was cited.", then it would be considered valid? I am also struggling to understand the Kumar example in the video...
@DestinyBoyles My understanding was that you have two rules, and Kumar arriving 17 minutes after the last ring falls outside the scope of those. I think of it like a language your computer can't process.
You know if that if someone was marked late, than they arrived 5+ minutes after the homeroom bell. You also know that if someone did not arrive 5+ minutes after the homeroom bell, than they were not marked late.
However, you were not given a rule for interpreting what happens when 5+ min late is the sufficient condition, so you have no information to make an inference. It's like your code throwing an error
it was pretty confusing watching this the first time. what helped me understand was focusing on the placement of the necessary and sufficient conditions.
Ok so because there was nothing indicating that Kumar was "late" in the second premise that makes the statement not true. Which leads to the conclusion being not true. Am I understanding that correctly?
The Kumar example was the most confusing but I think I understand it now.
Original sentence:
Students are cited as "late" only if they arrive more than five minutes past the last ring of the homeroom bell.
Lets say
A = late
B = 5+ minutes after homeroom bell
Another way of thinking about this is that "late" is the subset within the 5+ superset.
so in lawgic:
late --> 5+
/5+ --> /late
Now: Kumar arrived 17 min after the last ring of the homeroom bell.
So Kumar has membership in superset B (5+ min after homeroom bell), but that does not mean that he HAS to have membership in subset A (late). In the visual example, he would be within the 5+ superset circle, but outside of the "late" subset circle.
In practice, this might be because the teacher might have decided not to mark Kumar as late, or forgotten to mark him as late.
I might be wrong and feel free to respond, but this is how I understood it.
The contrapositive argument for the Melissa one is confusing. Is saying less not confusing negation with opposition? Would it not be "not more than 5 minutes late" rather than less? I mean, I know in effect that is less, so I guess negation and opposition can indeed be the same?
Does it matter which order the final english translation is in with regards to the sufficient and necessary conditions? Are they able to be mixed and matched? I assume yes because there was a lesson to highlight the various was equivalent ideas can be communicated in the english language versus Lawgic. Furthermore, the order doesn't seem to matter as long as the translation and negation steps are followed. Can someone clarify before I lose my marbles erasing and rewriting...?
For this, you have to understand necessity and sufficiency. Necessity means something is required for something else to happen. For example: “Alex gets a speeding ticket only if he speeds.”
So, the conclusion “Alex got a ticket, therefore he was speeding” is correct, because getting a ticket depends on him speeding. But speeding does not depend on whether he gets a ticket.
That’s why the conclusion “Alex was speeding, therefore he got a ticket” is incorrect just because he was speeding doesn’t mean he actually got caught and ticketed. In short, getting a ticket means he was speeding, but speeding doesn’t automatically mean he got a ticket. For something to be sufficient, it means it guarantees the result. For example: “If Alex speeds, then he will get a ticket.” That’s different from “only if,” because “if” makes speeding enough to cause the ticket, while “only if” just makes speeding required for a ticket.
@RazanTadros 7Sage needs to redo this lesson with this kind of context and adversarial perspective. Suffice to say, a lot are confused by the insufficient Kumar explanation.
the key to this one for me is the nuance of being CITED as late and being late... those are two different things. And being late doesn't guarantee you will be CITED as late.
could we take the contropostive to justify why kumar did not make the statement true? if kumar was not 17 minutes late than he was not late. this is false because he could be 16 minutes late.
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487 comments
The thing that helped me was thinking of the if and then as metrics in which to measure something. One is a measurement of time past 5 minutes. The other is a measurement of being late.
Since the measurement of time past 5 minutes is on the right then you are not measuring for that metric. (17 minutes is irrelevant in the 2nd premise)
Since the measurement of being late is on the left, then you are measuring for that metric.
Nothing was mentioned about whether or not he was late in the 2nd premise, just that he arrived 17 minutes after the bell, so no valid conclusion can be drawn because the sentence ha.
Likely Mistake Made: You tried to measure for the 5+ minutes metric but its on the right, you only measure for the metric on the left (late or not). You assumed that being late was equivalent to 5+ minutes but they are separate.
Reexplain kumar:
The rule is not saying that being more than 5 minutes late automatically gets you cited.
It is saying:
the condition should be "> 5 minutes" not "5+" because 5+ includes 5 not just more than 5.
5+ = 5,6,7,.... etc.
correct me if im wrong
To clarify, in the "only if" vs "if" statements, the sufficient and necessary clauses are different? For example;
If:
5+ min past bell is sufficient to say they are cited as late
Being cited as late is necessary to say they arrived 5+ min past the bell
Only if:
5+ min past bell is necessary to say they were cited as late
Being cited as late is sufficient to say they arrived 5+ min past the bell
So, necessary is the big bubble that catches all the conditions. So, by that logic, I feel like using "only if" turns the sufficient condition into a necessary condition. And both bubbles should be equivalent in size and trigger each other.
So like... if Elias arrived 17 minutes after the last bell, but he had a doctor's note or something. Some OTHER instance or possibility could be true in which he is arriving 5 minutes past the last bell but would not be considered late. In visual terms, he could be within the larger circle (more than 5 minutes after the bell), while not being in the smaller circle (cited as late).
@AidanW yeah this is my thought process too, I think its right. I am sorta visualizing the circles in my head as I read these to try and understand them.
The video explanation didn't specify that Kumar was a student so I thought the argument wasn't valid because it had an assumption that Kumar was a student...somehow reached the right answer in another way!
My brain hurt while trying to understand Kumar's case.
Anyways, what I understood from this lesson and from explanation in the comment section mostly (thanks to people clarifying it!), "only if" has exceptions. Kumar being late does not automatically put him in the subset of " cited as late". He could be. Or, he could not be cited as late; for example, he informed the school in advance about his medical appointment and arriving late, so the teacher would not put him as late. But the argument is silent in that regard.
Below is a basic example that helped me better understand Kumar's case:
We can NOT say:
Could be any animal e.g. dog, bird...
Being an animal is a necessity, but it is not sufficient for being a cat.
@Hfa Thank you....LOL
So even if Kumar arrived only six minutes after the bell, it would still be invalid to assume he would be marked late because he satisfies the necessary condition but not necessarily the sufficient condition?
Bro needs to go back to Kumar I’m still a little confused. Does that indicate that he only has the possibility of being cited as late?
@MilagrosZepeda I think it says that the only way he is guaranteed to be marked late is if he is more than five minutes past the last ring of the homeroom bell. Being 17 minutes after the last ring of the homeroom bell is different and doesn't trigger the conditional. It's really confusing because 17 minutes late is more than 5 minutes late, and you'd think it falls into that category. So what I learned is that if the argument contains "only if," then the conditional can only be triggered by saying the sufficient condition is happening in exactly the same way it was already stated in the argument. If it's not a word for word match, then it's probably the LSAT trying to trick you.
@BillyM_ So if the second premise listed said something along the lines of, "Kumar arrived 17 minutes after the last ring of the homeroom bell and was cited.", then it would be considered valid? I am also struggling to understand the Kumar example in the video...
@DestinyBoyles My understanding was that you have two rules, and Kumar arriving 17 minutes after the last ring falls outside the scope of those. I think of it like a language your computer can't process.
You know if that if someone was marked late, than they arrived 5+ minutes after the homeroom bell. You also know that if someone did not arrive 5+ minutes after the homeroom bell, than they were not marked late.
However, you were not given a rule for interpreting what happens when 5+ min late is the sufficient condition, so you have no information to make an inference. It's like your code throwing an error
it was pretty confusing watching this the first time. what helped me understand was focusing on the placement of the necessary and sufficient conditions.
If this helps anyone...
late -> 5+
So, if someone is marked late then it means they arrived 5+ minutes after the bell. But, it's not the only reason to arrive 5+ minutes after the bell.
Maybe you went to the doctor and arrived 5+ minutes after.
Maybe you had a basketball game and arrived 5+ minutes later.
Maybe you didn't go to school at all, came the next day and arrived 5+ minutes after the bell.
This is how I viewed it.
Ok so because there was nothing indicating that Kumar was "late" in the second premise that makes the statement not true. Which leads to the conclusion being not true. Am I understanding that correctly?
"Only if " is tricky. I see the "if" and automatically think that whatever comes after triggers the sufficient clause, but that's not correct.
The Kumar example was the most confusing but I think I understand it now.
Original sentence:
Students are cited as "late" only if they arrive more than five minutes past the last ring of the homeroom bell.
Lets say
A = late
B = 5+ minutes after homeroom bell
Another way of thinking about this is that "late" is the subset within the 5+ superset.
so in lawgic:
late --> 5+
/5+ --> /late
Now: Kumar arrived 17 min after the last ring of the homeroom bell.
So Kumar has membership in superset B (5+ min after homeroom bell), but that does not mean that he HAS to have membership in subset A (late). In the visual example, he would be within the 5+ superset circle, but outside of the "late" subset circle.
In practice, this might be because the teacher might have decided not to mark Kumar as late, or forgotten to mark him as late.
I might be wrong and feel free to respond, but this is how I understood it.
@kadeleon This helped me a lot. Thanks!
@kadeleon thnx for this I was so lost
So does an 'if' statement sort of flip the order of the conditional? How does this work for the Kumar example:
"students are cited as late only if they arrive 5+ minutes past last ring"
Let's say that being cited late = A
Being 5+ mins late = B
An 'only if' statement looks like A --> B
An 'if' statement would look like B --> A
It seems intuitive to read a conditional from left to right as English is read, so does an 'if' statement flip the order?
@SeamusMcCarthy I think you are correct about
this
@SeamusMcCarthy "If" always introduces the sufficient condition. "Only if" introduces the necessary.
If X, then Y.
Only if Y, X.
Y if X.
X only if Y.
All of those mean the same thing:
X --> Y
The contrapositive argument for the Melissa one is confusing. Is saying less not confusing negation with opposition? Would it not be "not more than 5 minutes late" rather than less? I mean, I know in effect that is less, so I guess negation and opposition can indeed be the same?
I am so cooked after that Kumar one ngl...
Sooo.. Kumar could be cited as late, but its not necessary? Even though he is in the circles sufficiently, he's not necessarily constrained to them?
I made flash cards to help memorize group 1-4 conditional indicators, thought I’d share in case it would be helpful to anyone else. I’m redoing this course after getting through most of it and taking the lsat and not doing as well as I hoped. Looking back I realize how important it is to know these. https://quizlet.com/1153975729/lsat-7sage-conditional-indicators-to-share-flash-cards/?i=71yhg9&x=1jqY
Where would Kumar be in the circle set then? In the "arrive 5+ mins after" circle?
Does it matter which order the final english translation is in with regards to the sufficient and necessary conditions? Are they able to be mixed and matched? I assume yes because there was a lesson to highlight the various was equivalent ideas can be communicated in the english language versus Lawgic. Furthermore, the order doesn't seem to matter as long as the translation and negation steps are followed. Can someone clarify before I lose my marbles erasing and rewriting...?
In conditional reasoning, you can't use necessary condition to prove sufficient condition only if you are using it in the contrapositive.
Is that correct?
@Danaizha I think so, only if you negate the sufficient condition
For this, you have to understand necessity and sufficiency. Necessity means something is required for something else to happen. For example: “Alex gets a speeding ticket only if he speeds.”
So, the conclusion “Alex got a ticket, therefore he was speeding” is correct, because getting a ticket depends on him speeding. But speeding does not depend on whether he gets a ticket.
That’s why the conclusion “Alex was speeding, therefore he got a ticket” is incorrect just because he was speeding doesn’t mean he actually got caught and ticketed. In short, getting a ticket means he was speeding, but speeding doesn’t automatically mean he got a ticket. For something to be sufficient, it means it guarantees the result. For example: “If Alex speeds, then he will get a ticket.” That’s different from “only if,” because “if” makes speeding enough to cause the ticket, while “only if” just makes speeding required for a ticket.
@RazanTadros This helped me because I didn't think of the idea of not getting caught.
@RazanTadros Thank you that helps a lot
@RazanTadros Thank you. Really helpful!
@RazanTadros Thanks! Very helpful.
@RazanTadros 7Sage needs to redo this lesson with this kind of context and adversarial perspective. Suffice to say, a lot are confused by the insufficient Kumar explanation.
the key to this one for me is the nuance of being CITED as late and being late... those are two different things. And being late doesn't guarantee you will be CITED as late.
could we take the contropostive to justify why kumar did not make the statement true? if kumar was not 17 minutes late than he was not late. this is false because he could be 16 minutes late.