I understand that we can assume that Elias arrived 5+ minutes late and now that I've seen it I understand why the Kumar example is wrong, I just don't think I'd actually be able to see that on a more complex LSAT question. Also I need to see it visually and I just simply don't have the time to draw circles for every necessary assumption question on the test...
I believe there's a small mistake in the contrapositive argument portion, I think the negation of "arrive more than five minutes past the last ring of the homeroom bell" is most accurately negated to "arrived five minutes or less than the homeroom bell" instead of "less than five minutes". The negation in the video ignores that it is possible to arrive exactly five minutes.
Here's what helped me understand (This is for my own note taking, but feel free to enjoy if it helps)
The biggest thing that made the Kumar example click is the difference between subset and superset.
Sufficient conditions are the subset, and necessary conditions are the super set.
My translation: Membership in the subset is good enough (Sufficient assumption) for membership in the superset, but is not necessary (Necessary assumption)
Membership in the superset is necessary (necessary assumption) but it is not good enough (sufficient) to be apart of the subset.
If y'all are confused, it helped me to think of an imaginary example as to why the logic is invalid to say that Kumar will be marked late.
Let's pretend he arrived 17 minutes late, but with a doctor's note, which the school accepts to mean he is not counted as late. He can ONLY be counted late if he is 5+ minutes late, but he is not REQUIRED to be counted late--here because of our made-up doctor's note. The logic does not ABSOLUTELY DEMAND he be marked late, as it can easily be proven broken with our example. :)
Wow! Sufficiency vs Necessity finally clicked with this lesson. The late Kumar example really took it home. It's still a bit touch and go but something definitely clicked!
The example with KUMAR is not making sense to me because it clearly states he arrived 5 minutes past the last ring (he arrived 17 minutes after the last ring), so how would he not be cited as late?????
For those of you who noticed that "Only" is mentioned both in the group 1 indicators and in the group 2 indicators the way that I found that is simple to remember it is "THE ONLY time it is group 1 is when it says THE ONLY". Every other time that only is used as an indicator it is referring to group 2 (only, only if, only where, only when). For some reason I naturally want to start out that sentence with "the only" every time which makes it easy because it matches.
Group 2 Logical Indicators
(R.O.M.A)
-Requires (not listed but if written "x requires y" then it can be same type of relationship)
-Only, only if, only when, only where
-Must
-Always
Note: to read carefully when the text says "X is required Y" by instead of requires. In the way this is written the required part would actually be in front of the word required instead of following it.
I appreciate the structure that they are trying to teach here. However, outside of this structured environment (where they are trying to teach a specific idea), I get tripped up on the problem that Melissa and Elias are never defined as students. When is it safe to make assumptions that are not clearly stated in the argument?
Is L -> 5+ the same thing as saying "IF one is marked late, then they must have arrived more than five minutes past the last ring?"
In other words, if you were to remove the necessary indicator and insert a sufficient indicator in front of the sufficient condition, that would be the exact same argument, right?
found the trouble in the word "are". Had it been "must be" or "always are" this would be a different scenario. Being cited as late guarantees that a student arrived 5+ past, because thats the rule for that particular situation. However, being more that 5 minutes late doesn't guarantee being cited as late.
It took me a while to understand the Kumar example, but what finally made it click was focusing on the LAWGIC language instead of the words themselves.
So two valid arguments based on the conditions given. Students cited late ONLY IF they are more than 5 minutes late. Elias was cited late. So Elias arrived more than 5 minutes last. Or the contrapositive not cited late then not arriving more than 5 minutes past the last ring. The confusing part is why would 17 minutes late not be in more than 5 minutes late. The only thing I can think of is because we are solely going based on what they give us.
So even if we know 17 is more than 5 since they did not explicitly say that we ignore it. Correct me if I’m wrong. So unless it says more than 5 minutes late or the contra positive it is not a a valid argument. Correct me if I’m wrong
DeniseDenault's comment explained "only if" as a minimum requirement. That along with drawing the visual make it click for me. 5+ being the larger circle and Late being the smaller. You can put being 17 min past anywhere in the 5+ circle, including the L circle, but it does not have to make sense.
Seeing the visual helped me connect the dots. Being 5+ puts you in the circle but it does not NECESSARILY mean you will also be in the smaller L circle. It's the minimum condition that needs to be met for the possibility of being cited as late to occur.
Wow, the Kumar example made a LOT more sense after the Elias example was shown. If the sufficient condition is triggered (being cited as late), then the necessary condition occurs (arriving 5 minutes past bell). Arriving 5 minutes past the bell doesn't guarantee you'll be cited as "late". Perhaps the teacher was not there on time and wasn't able to see you come in late. Here's an example I think is valid.
A movie can be rated R only if the content is deemed too scary for children under 17.
The movie "Saw" is rated R.
Therefore, "Saw" has content that is deemed too scary for children under 17.
It wouldn't make sense for the argument to be 1 --> "Saw has scary content" --> "Saw" is rated R because the necessary condition of the film having scary content for a certain age group wasn't met. Imagine rating a movie R without meeting the necessary criteria for the rating. It doesn't follow that an R rated movie WOULDN'T have certain parameters.
A sufficient --> necessary example would be
A movie can be rated R if the content is deemed too scary for children under 17.
The movie "Saw" was deemed too scary for children under 17.
Therefore, "Saw" has an R rating.
I think this makes sense. If I'm wrong someone correct me! I hope I finally got it.
Confused at first, but once you see the visual diagram for Elias, it makes sense; arriving 5 minutes after is necessary for being cited as late, but not sufficient (you don't know for sure they were cited just because they showed up 5 minutes after).
Learning to prioritize the form rather than the content in your brain is the tricky part
Is there ever going to be an instance where we get in trouble with details such as "more than" 5 minutes late? Because, technically, if Melissa is exactly 5 minutes late, she isn't more than 5 minutes late. She also isn't less than 5 minutes late as set up in the contrapositive.
Does anyone think they may be able to help me understand this. I get the point that it doesn't guarantee anything but I don't understand how when one is reading the text that they came to that conclusion so quickly. To me, I understood it as you will get cited as late if you come in past 5 minutes of the bell, and he was 17 minutes late. So what I'm asking is do we have to assume that nothing is guaranteed for necessary conditions, ex. Kumar could get excused from the late arrival, he only gets cited when he is caught. If that's a correct assumption how do I notice this more quickly?
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387 comments
I understand that we can assume that Elias arrived 5+ minutes late and now that I've seen it I understand why the Kumar example is wrong, I just don't think I'd actually be able to see that on a more complex LSAT question. Also I need to see it visually and I just simply don't have the time to draw circles for every necessary assumption question on the test...
I believe there's a small mistake in the contrapositive argument portion, I think the negation of "arrive more than five minutes past the last ring of the homeroom bell" is most accurately negated to "arrived five minutes or less than the homeroom bell" instead of "less than five minutes". The negation in the video ignores that it is possible to arrive exactly five minutes.
Here's what helped me understand (This is for my own note taking, but feel free to enjoy if it helps)
The biggest thing that made the Kumar example click is the difference between subset and superset.
Sufficient conditions are the subset, and necessary conditions are the super set.
My translation: Membership in the subset is good enough (Sufficient assumption) for membership in the superset, but is not necessary (Necessary assumption)
Membership in the superset is necessary (necessary assumption) but it is not good enough (sufficient) to be apart of the subset.
If y'all are confused, it helped me to think of an imaginary example as to why the logic is invalid to say that Kumar will be marked late.
Let's pretend he arrived 17 minutes late, but with a doctor's note, which the school accepts to mean he is not counted as late. He can ONLY be counted late if he is 5+ minutes late, but he is not REQUIRED to be counted late--here because of our made-up doctor's note. The logic does not ABSOLUTELY DEMAND he be marked late, as it can easily be proven broken with our example. :)
Why wasn't a pictorial representation done for the Kumar's case???
Wow! Sufficiency vs Necessity finally clicked with this lesson. The late Kumar example really took it home. It's still a bit touch and go but something definitely clicked!
The example with KUMAR is not making sense to me because it clearly states he arrived 5 minutes past the last ring (he arrived 17 minutes after the last ring), so how would he not be cited as late?????
"One knows the way I feel tonight only if they are lonely." -Roy Orbison
For those of you who noticed that "Only" is mentioned both in the group 1 indicators and in the group 2 indicators the way that I found that is simple to remember it is "THE ONLY time it is group 1 is when it says THE ONLY". Every other time that only is used as an indicator it is referring to group 2 (only, only if, only where, only when). For some reason I naturally want to start out that sentence with "the only" every time which makes it easy because it matches.
Group 2 Logical Indicators
(R.O.M.A)
-Requires (not listed but if written "x requires y" then it can be same type of relationship)
-Only, only if, only when, only where
-Must
-Always
Note: to read carefully when the text says "X is required Y" by instead of requires. In the way this is written the required part would actually be in front of the word required instead of following it.
I appreciate the structure that they are trying to teach here. However, outside of this structured environment (where they are trying to teach a specific idea), I get tripped up on the problem that Melissa and Elias are never defined as students. When is it safe to make assumptions that are not clearly stated in the argument?
Is L -> 5+ the same thing as saying "IF one is marked late, then they must have arrived more than five minutes past the last ring?"
In other words, if you were to remove the necessary indicator and insert a sufficient indicator in front of the sufficient condition, that would be the exact same argument, right?
Switching the Subset and Superset is the only thing that makes sense here.
IF: 5+ -> late. (if you're 5+ min after bell, you're late.)
ONLY IF: late -> 5+ (if you're late, you're 5+ min after bell).
found the trouble in the word "are". Had it been "must be" or "always are" this would be a different scenario. Being cited as late guarantees that a student arrived 5+ past, because thats the rule for that particular situation. However, being more that 5 minutes late doesn't guarantee being cited as late.
Would a more accurate translation be 6+? The necessary condition says "more than" 5 minutes late. So, 5 mins is not late.
The superset and subset made the Kumar example click. He can be late however that doesn't automatically mean he will be cited as late.
It took me a while to understand the Kumar example, but what finally made it click was focusing on the LAWGIC language instead of the words themselves.
If A then B is valid
If B then A is invalid
VALID
(A) If Cited Late then
(B) Must have arrived 5 min past the bell
INVALID
(B) If arrived 5 min past the bell then
(A) you must be cited late
So two valid arguments based on the conditions given. Students cited late ONLY IF they are more than 5 minutes late. Elias was cited late. So Elias arrived more than 5 minutes last. Or the contrapositive not cited late then not arriving more than 5 minutes past the last ring. The confusing part is why would 17 minutes late not be in more than 5 minutes late. The only thing I can think of is because we are solely going based on what they give us.
So even if we know 17 is more than 5 since they did not explicitly say that we ignore it. Correct me if I’m wrong. So unless it says more than 5 minutes late or the contra positive it is not a a valid argument. Correct me if I’m wrong
DeniseDenault's comment explained "only if" as a minimum requirement. That along with drawing the visual make it click for me. 5+ being the larger circle and Late being the smaller. You can put being 17 min past anywhere in the 5+ circle, including the L circle, but it does not have to make sense.
Seeing the visual helped me connect the dots. Being 5+ puts you in the circle but it does not NECESSARILY mean you will also be in the smaller L circle. It's the minimum condition that needs to be met for the possibility of being cited as late to occur.
Wow, the Kumar example made a LOT more sense after the Elias example was shown. If the sufficient condition is triggered (being cited as late), then the necessary condition occurs (arriving 5 minutes past bell). Arriving 5 minutes past the bell doesn't guarantee you'll be cited as "late". Perhaps the teacher was not there on time and wasn't able to see you come in late. Here's an example I think is valid.
A movie can be rated R only if the content is deemed too scary for children under 17.
The movie "Saw" is rated R.
Therefore, "Saw" has content that is deemed too scary for children under 17.
It wouldn't make sense for the argument to be 1 --> "Saw has scary content" --> "Saw" is rated R because the necessary condition of the film having scary content for a certain age group wasn't met. Imagine rating a movie R without meeting the necessary criteria for the rating. It doesn't follow that an R rated movie WOULDN'T have certain parameters.
A sufficient --> necessary example would be
A movie can be rated R if the content is deemed too scary for children under 17.
The movie "Saw" was deemed too scary for children under 17.
Therefore, "Saw" has an R rating.
I think this makes sense. If I'm wrong someone correct me! I hope I finally got it.
It would be helpful to see a diagram for Kumar
Wow this makes my brain hurt
Confused at first, but once you see the visual diagram for Elias, it makes sense; arriving 5 minutes after is necessary for being cited as late, but not sufficient (you don't know for sure they were cited just because they showed up 5 minutes after).
Learning to prioritize the form rather than the content in your brain is the tricky part
#help
Is there ever going to be an instance where we get in trouble with details such as "more than" 5 minutes late? Because, technically, if Melissa is exactly 5 minutes late, she isn't more than 5 minutes late. She also isn't less than 5 minutes late as set up in the contrapositive.
So, the sufficient condition is the "trigger" to allow us to say something about the larger, necessary condition (superset).
Does anyone think they may be able to help me understand this. I get the point that it doesn't guarantee anything but I don't understand how when one is reading the text that they came to that conclusion so quickly. To me, I understood it as you will get cited as late if you come in past 5 minutes of the bell, and he was 17 minutes late. So what I'm asking is do we have to assume that nothing is guaranteed for necessary conditions, ex. Kumar could get excused from the late arrival, he only gets cited when he is caught. If that's a correct assumption how do I notice this more quickly?