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?
it was pretty confusing watching this the first time. what helped me understand was focusing on the placement of the necessary and sufficient conditions.
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.
@nbarchaim It would not be. We only know one rule of the classroom. That if you were cited as late, then you were 5+ minutes late. Since we only know Kumar was 17 minutes late, we can't make any inferences about how he was cited. Maybe he always shows up 17 minutes late, so the teacher doesn't mark him down. Maybe Kumar is a TA and can't be cited as late. There is no way to make a valid conclusion that he was cited as late.
I don't know if I'm getting this right, but which is which? Is the subset the necessary condition or the superset? Or does it depend on its (the 2 claims') relation to each other? Someone help, I'm a bit confused....
Students are cited as "late" only if they arrive more than five minutes past the last ring of the homeroom bell.
late -> 5+(this is because the being 5 or more minutes past the last ring of homeroom bell is the necessary condition since it's after the "only if"... i.e. it's the large circle, the "mammal" circle, so it's on the right side of the arrow)
now the below lays out the sufficient version instead of the necessary verbiage above.
Students are cited as "late" if they arrive more than five minutes past the last ring of the homeroom bell.
5+ -> late (this is because what comes after "if" is what is sufficient so it's on the left side of the arrow unlike the first sentence which demonstrates necessity so it's on the right side of the arrow)
Applying the logic in the first statement to this next one: Kumar arrived 17 mins late. That doesn't mean the student is automatically marked as late because it's not sufficient, it's just necessary. It's just one possible reason for being marked late, it's not entirely dependent on that one singular factor.
Applying the logic in the second statement to "Kumar arrived 17 mins late". Kumar MUST be marked late because he is more than 5 minutes late. It is sufficient, it's specific enough like "cats are mammals" (and those circles in that example). If he doesn't want to be marked late, he shouldn't be more than 5 minutes late.
@EliseBoessler Right! And because the example statement uses the "only if" version, that's the meaning of the statement in this lesson. The "If" version is what a lot of people commonly misread "only if" to mean.
Remember! A claim that meets the necessary condition (Kumar late) does NOTguarantee the sufficient condition (citation). It only creates the possibility for the sufficient condition to trigger. "COULD BE TRUE"
Kumar late? The teacher now has the option to cite, but may choose not to. Kumar not late? Teach does not have the option to cite at all.
You can actually visualize this one with circles. Citation smaller circle within late. When Kumar arrives late, he's necessarily inside the late circle but could be anywhere inside the circle. He could be in a different subset that says "gets pizza." Or he could be in the circle of citation.
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473 comments
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.
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?
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.
"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!
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 sighted 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.
WOW, After two years of studying for the LSAT and doing it twice, something inside my brain clicked. WOW just wow.
Would it be accurate to conclude that Kumar was probably cited as late?
@nbarchaim It would not be. We only know one rule of the classroom. That if you were cited as late, then you were 5+ minutes late. Since we only know Kumar was 17 minutes late, we can't make any inferences about how he was cited. Maybe he always shows up 17 minutes late, so the teacher doesn't mark him down. Maybe Kumar is a TA and can't be cited as late. There is no way to make a valid conclusion that he was cited as late.
@EthanJLazzara thank you so much this clicked for me!!!!
The opposite of arriving more than five minutes late is arriving just five minutes or less than five minutes late.
I don't know if I'm getting this right, but which is which? Is the subset the necessary condition or the superset? Or does it depend on its (the 2 claims') relation to each other? Someone help, I'm a bit confused....
@Isabel.C The sufficient condition is the subset (the smaller circle within the bigger circle).
This has absolutely helped me start consistently getting inference questions correct.
Can someone tell me if this is correct?
Students are cited as "late" only if they arrive more than five minutes past the last ring of the homeroom bell.
late -> 5+ (this is because the being 5 or more minutes past the last ring of homeroom bell is the necessary condition since it's after the "only if"... i.e. it's the large circle, the "mammal" circle, so it's on the right side of the arrow)
now the below lays out the sufficient version instead of the necessary verbiage above.
Students are cited as "late" if they arrive more than five minutes past the last ring of the homeroom bell.
5+ -> late (this is because what comes after "if" is what is sufficient so it's on the left side of the arrow unlike the first sentence which demonstrates necessity so it's on the right side of the arrow)
Applying the logic in the first statement to this next one: Kumar arrived 17 mins late. That doesn't mean the student is automatically marked as late because it's not sufficient, it's just necessary. It's just one possible reason for being marked late, it's not entirely dependent on that one singular factor.
Applying the logic in the second statement to "Kumar arrived 17 mins late". Kumar MUST be marked late because he is more than 5 minutes late. It is sufficient, it's specific enough like "cats are mammals" (and those circles in that example). If he doesn't want to be marked late, he shouldn't be more than 5 minutes late.
Can someone confirm if this is sound? Thank you!!
@EliseBoessler Right! And because the example statement uses the "only if" version, that's the meaning of the statement in this lesson. The "If" version is what a lot of people commonly misread "only if" to mean.
Remember! A claim that meets the necessary condition (Kumar late) does NOT guarantee the sufficient condition (citation). It only creates the possibility for the sufficient condition to trigger. "COULD BE TRUE"
Kumar late? The teacher now has the option to cite, but may choose not to. Kumar not late? Teach does not have the option to cite at all.
You can actually visualize this one with circles. Citation smaller circle within late. When Kumar arrives late, he's necessarily inside the late circle but could be anywhere inside the circle. He could be in a different subset that says "gets pizza." Or he could be in the circle of citation.