It's strange and frustrating that this lesson doesn't teach you how to actually diagram this one correctly in Lawgic. Very difficult to be told we were wrong, not be shown how to map this out accurately, and then be thrown into the quiz in the next section.
So, I see an error. In the Melissa example, the video says that the contrapositive is that "Melissa arrived less than five minutes past the last ring." I think this error confuses opposition and negation.
I think the proper contrapositive would be "Melissa did not arrive more than five minutes past the last ring of the homeroom bell."
Put differently: Melissa arrived five minutes or less past the last ring.
Note that the original argument says "more than five minutes past." It DOES NOT say "five minutes OR more." Big difference, and one that will matter on tricky questions!
Ah, my greatest weakness. Confusing necessary for sufficient. Being the necessary condition cannot trigger the sufficient condition. I guessed wrong, and then when the presentation visualized it, I had to smack my forehead.
It's worth noting that a tricky question based around the conditional "Students are cited as "late" only if they arrive more than five minutes past the last ring of the homeroom bell," could lay a trap with with the "more than five minutes" part of the necessary condition. The "more than five minutes" negated is not "less than five minutes," it's "NOT more than five minutes" or "less than OR EQUAL TO five minutes."
While valid, your expansion of the contrapositive argument form is incomplete in a way that might be misleading. It would be be equally valid if it said "Melissa arrived five minutes past the last ring," or, more completely, "Melissa arrived less than or equal to five minutes past the last ring."
Correct me if im wrong but essentially what this saying is that in the 'only if' sentence, the student does not have to be marked as late. Them arriving 5+ minutes late does not mean that they will be cited as late, just that the now meet the condition and COULD be cited as late
Whereas with the 'if' sentence, if they're more than 5 minutes late, they WILL be marked as late
Basically, 'only if' -> they've now met the condition and the thing could happen
I understand the RULE. I got to the right answer knowing the rule that necessary assumption cannot trigger the sufficient clause. But logically idk what that means, I just know the rule.
I'm confused... Because it says only if a student is more than five minutes late. Kumar was more than five minutes late. Why does it not apply??? Help lol why does the only mean it doesn't apply to him?
@Mandeemack I'd really recommend going back to the 30min Conditional Video and watching it again. BC this is where I'm pulling my info from, but essentially the formula of how this works is that ONLY the sufficient can trigger the necessary. The necessary canNOT trigger the sufficient.
Ex: Students are cited late (A) > 5 mins past bell (B)
The Premise states "Kumar is 17 Mins Late (B) > therefore will be cited late (A).
But this is INVALID, because B cannot trigger A.
This WOULD become Valid, if the premise was stated instead as:
Kumar was 17mins EARLY, therefore he won't be cited late. (bc that's the contrapositive of the main statement). Formula would be /b > /a.
OR
Elias was cited late (A) > arrived 5 mins past bell (B)
Which matches the original argument.
It really helps for me to break it down as algebraic formulas and not think about what they're "actually" saying at first.
-- So identify the main formula the argument is making. Then identify the formula of the premise that you're trying to determine if it's valid or invalid. THEN, compare it to the 4 formulas provided in the conditional video and you'll get your answer.
Two of those formulas are used in this example alone.
I dont know if someone else commented this but a helpful way to think about it is to reword the sentence, "A student canonly be late if he/she arrives more than 5 minutes after the bell"
Maybe this will help: If Kumar is 17 mins late, he qualifies to be marked late, but he has only landed himself in the necessary condition/superset/big circle, not confirmed to be in the subset/sufficient
Are the 6 indicator words listed the only ones that come up on the LSAT? When learning conditional logic (albeit for discrete math) we we taught to say A->B as "A implies B".
Ex:
If you have eyes, you can see.
Having eyes implies you can see.
Having eyes -> You can see
Does it not being one of the 6 listed mean it doesn't really show up on the LSAT, or is list of words given supposed to be non-exhaustive?
As JY mentioned in the beginning of this module, the list of terms is overinclusive/underinclusive.
This means that some of these indicators are a bigger list than what may show up on the LSAT, or there may be more different indicators than what you may have been shown in this module. A good strong foundational understanding of these arguments will allow you to decipher different indicator words, and with practice, you'll see others.
So I could be wrong but the Kumar argument was invalid because he was 15 min late and not 5 min late? because it said ONLY IF they arrive more than 5 min past the ring? are we saying its invalid because we don't know what happens if hes 15 min late? Sorry if this is a silly question !
@Mr.Coolguy No, the Kumar example was invalid because the necessary condition in the example (ie him arriving 17 minutes after the bell) functionally doesn't trigger the sufficient condition of being marked late.
Consider: maybe Kumar had a note from his mom, was in a meeting with the Principal or the teacher just forgot to mark him late. The act of "being late" doesn't guarantee being "marked late". I hope that helps!
@EllieErnst for the argument to be valid it would be rewritten either with a sufficient necessity indicator, like in the video, or something like this:
Students are cited as "late" only if they arrive more than five minutes past the last ring of the homeroom bell. Kumar was cited as late. Therefore, he arrived more than 5 minutes past the last bell
So if I am understanding correctly, only if implies that being more than 5 minutes late is the first of potentially multiple factors that could contribute to being marked late? So If Kumar is less than 5 minutes late he for sure won't be marked as late but if he is 17 minutes late he may or may not be marked as late depending on many other factors that we don't know about (eg. maybe he called into the front office and said he'd be late so his tardiness was excused, or maybe he was completing an errand for the professor) or any of a million other possible reasons. But basically being more than 5 minutes late is the first factor that contributes towards possibly being marked as late.
@AmyEK Yes. As a visual learner I looked at it using the superset and subset visual model. The superset is 'coming 5 minutes + after the ring of the bell', and the subset is 'marked as late'. If a member is in 'marked as late', then the member NECESSARILY came 5+ minutes after the ring of the bell.
But if the member is outside the 'coming 5+ minutes after the ring of the bell' superset, it is IMPOSSIBLE to be marked late.
I don't know if this makes more sense or confuses things, hopefully the former! Good luck with your studying!
For anyone else confused on the logic of the example. My simpleton brain explained it like a teacher will only CITE you as late only if they NOTICE you are more than 5 minutes late. Kumar was late but he snuck into class 17 minutes late and the teacher did not notice Kumar because he is super sneaky. That is the only thing I can think of where Kumar wouldn't be cited.
The way I thought about it was to think about where the emphasis is. The emphasis is on being noted as "Late" (the sufficient - inner circle), then they must logically be within the "5+ arrival" (the necessary - outer circle). btw, the way I memorized the circles was like this: Alphabetically, N comes first, so it is the first circle (outer circle) and S comes second, so it is the second circle (inner circle).
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.
Likely Mistake Made: You tried to measure for the 5+ minutes metric but it’s 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.
523 comments
helpful rewrite from:
Students are late only if they arrive more than five minutes after the bell.
TO
Only if students arrive more than five minutes after the last bell can they be late.
It's strange and frustrating that this lesson doesn't teach you how to actually diagram this one correctly in Lawgic. Very difficult to be told we were wrong, not be shown how to map this out accurately, and then be thrown into the quiz in the next section.
So, I see an error. In the Melissa example, the video says that the contrapositive is that "Melissa arrived less than five minutes past the last ring." I think this error confuses opposition and negation.
I think the proper contrapositive would be "Melissa did not arrive more than five minutes past the last ring of the homeroom bell."
Put differently: Melissa arrived five minutes or less past the last ring.
Note that the original argument says "more than five minutes past." It DOES NOT say "five minutes OR more." Big difference, and one that will matter on tricky questions!
Def flagging this section and coming back like 20 times.
Ah, my greatest weakness. Confusing necessary for sufficient. Being the necessary condition cannot trigger the sufficient condition. I guessed wrong, and then when the presentation visualized it, I had to smack my forehead.
I swear this section makes me want to take an ashwagandha, I cannot!
It's worth noting that a tricky question based around the conditional "Students are cited as "late" only if they arrive more than five minutes past the last ring of the homeroom bell," could lay a trap with with the "more than five minutes" part of the necessary condition. The "more than five minutes" negated is not "less than five minutes," it's "NOT more than five minutes" or "less than OR EQUAL TO five minutes."
While valid, your expansion of the contrapositive argument form is incomplete in a way that might be misleading. It would be be equally valid if it said "Melissa arrived five minutes past the last ring," or, more completely, "Melissa arrived less than or equal to five minutes past the last ring."
Is a right way to think about this: valid arguments trigger the sufficient condition or negate the necessary condition?
Correct me if im wrong but essentially what this saying is that in the 'only if' sentence, the student does not have to be marked as late. Them arriving 5+ minutes late does not mean that they will be cited as late, just that the now meet the condition and COULD be cited as late
Whereas with the 'if' sentence, if they're more than 5 minutes late, they WILL be marked as late
Basically, 'only if' -> they've now met the condition and the thing could happen
'if' -> the thing will happen
Is that right or am I way off
I understand the RULE. I got to the right answer knowing the rule that necessary assumption cannot trigger the sufficient clause. But logically idk what that means, I just know the rule.
I guessed that it was wrong but because they never stated Kumar was a student
I'm confused... Because it says only if a student is more than five minutes late. Kumar was more than five minutes late. Why does it not apply??? Help lol why does the only mean it doesn't apply to him?
@Mandeemack I'd really recommend going back to the 30min Conditional Video and watching it again. BC this is where I'm pulling my info from, but essentially the formula of how this works is that ONLY the sufficient can trigger the necessary. The necessary canNOT trigger the sufficient.
Ex: Students are cited late (A) > 5 mins past bell (B)
The Premise states "Kumar is 17 Mins Late (B) > therefore will be cited late (A).
But this is INVALID, because B cannot trigger A.
This WOULD become Valid, if the premise was stated instead as:
Kumar was 17mins EARLY, therefore he won't be cited late. (bc that's the contrapositive of the main statement). Formula would be /b > /a.
OR
Elias was cited late (A) > arrived 5 mins past bell (B)
Which matches the original argument.
It really helps for me to break it down as algebraic formulas and not think about what they're "actually" saying at first.
-- So identify the main formula the argument is making. Then identify the formula of the premise that you're trying to determine if it's valid or invalid. THEN, compare it to the 4 formulas provided in the conditional video and you'll get your answer.
Two of those formulas are used in this example alone.
Hope this helps!
I dont know if someone else commented this but a helpful way to think about it is to reword the sentence, "A student can only be late if he/she arrives more than 5 minutes after the bell"
Maybe this will help: If Kumar is 17 mins late, he qualifies to be marked late, but he has only landed himself in the necessary condition/superset/big circle, not confirmed to be in the subset/sufficient
Are the 6 indicator words listed the only ones that come up on the LSAT? When learning conditional logic (albeit for discrete math) we we taught to say A->B as "A implies B".
Ex:
If you have eyes, you can see.
Having eyes implies you can see.
Having eyes -> You can see
Does it not being one of the 6 listed mean it doesn't really show up on the LSAT, or is list of words given supposed to be non-exhaustive?
@willdhorn,
As JY mentioned in the beginning of this module, the list of terms is overinclusive/underinclusive.
This means that some of these indicators are a bigger list than what may show up on the LSAT, or there may be more different indicators than what you may have been shown in this module. A good strong foundational understanding of these arguments will allow you to decipher different indicator words, and with practice, you'll see others.
So I could be wrong but the Kumar argument was invalid because he was 15 min late and not 5 min late? because it said ONLY IF they arrive more than 5 min past the ring? are we saying its invalid because we don't know what happens if hes 15 min late? Sorry if this is a silly question !
@Mr.Coolguy No, the Kumar example was invalid because the necessary condition in the example (ie him arriving 17 minutes after the bell) functionally doesn't trigger the sufficient condition of being marked late.
Consider: maybe Kumar had a note from his mom, was in a meeting with the Principal or the teacher just forgot to mark him late. The act of "being late" doesn't guarantee being "marked late". I hope that helps!
@RyanAlexander That actually does help! thank you sm!!
@RyanAlexander This one helped me understand it. Thank you sm!
@RyanAlexander This was extremely helpful! Thank you!
This one really got me... But I found a helpful trick:
ONLY IF states a NECESSARY condition
Necesary conditions are always the superset.
you can rewrite 'only if' statements to 'if then' statements
Ex. Students are cited as "late" only if they arrive more than five minutes past the last ring of the homeroom bell.
This is the same as:
If Students are cited as "late" then they arrive more than five minutes past the last ring of the homeroom bell.
these are the same but the second one makes the necessary condition much clearer.
Late --> 5+
How would the Kumar example need to be worded to satisfy both the necessary and sufficient conditions?
Students are cited as "late" only if they arrive more than five minutes past the last ring of the homeroom bell. Kumar was cited as late. Therefore, he arrived more than 5 minutes past the last bell
So if I am understanding correctly, only if implies that being more than 5 minutes late is the first of potentially multiple factors that could contribute to being marked late? So If Kumar is less than 5 minutes late he for sure won't be marked as late but if he is 17 minutes late he may or may not be marked as late depending on many other factors that we don't know about (eg. maybe he called into the front office and said he'd be late so his tardiness was excused, or maybe he was completing an errand for the professor) or any of a million other possible reasons. But basically being more than 5 minutes late is the first factor that contributes towards possibly being marked as late.
@AmyEK Yes. As a visual learner I looked at it using the superset and subset visual model. The superset is 'coming 5 minutes + after the ring of the bell', and the subset is 'marked as late'. If a member is in 'marked as late', then the member NECESSARILY came 5+ minutes after the ring of the bell.
But if the member is outside the 'coming 5+ minutes after the ring of the bell' superset, it is IMPOSSIBLE to be marked late.
I don't know if this makes more sense or confuses things, hopefully the former! Good luck with your studying!
For anyone else confused on the logic of the example. My simpleton brain explained it like a teacher will only CITE you as late only if they NOTICE you are more than 5 minutes late. Kumar was late but he snuck into class 17 minutes late and the teacher did not notice Kumar because he is super sneaky. That is the only thing I can think of where Kumar wouldn't be cited.
@joelsmith thank you! I was also confused by that argument
@joelsmith Also, you could say that maybe he just didn't get cited "late" for the following reasons:
Maybe he was excused this time.
Maybe students get free passes.
Maybe the teacher forgot to mark him.
Maybe he snuck into class without being caught (like you mentioned)
Being 5 minutes late is just a requirement for being late, doesn't mean every student actually will be cited.
The way I thought about it was to think about where the emphasis is. The emphasis is on being noted as "Late" (the sufficient - inner circle), then they must logically be within the "5+ arrival" (the necessary - outer circle). btw, the way I memorized the circles was like this: Alphabetically, N comes first, so it is the first circle (outer circle) and S comes second, so it is the second circle (inner circle).
@AmirAlavi this is good. you also just made me think s = smaller circle
Wait so then why do you take the contrapositive for translation if the claim isn't actually valid that way?
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.
Likely Mistake Made: You tried to measure for the 5+ minutes metric but it’s 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.
@pmartinez95 so is it always the sufficient the concept being measured because the necessary condition is the result of the sufficient trigger?
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