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.
Let me see if I’m grasping this correctly… the example with Kumar arriving 17 minutes after the bell doesn’t allow us to conclude he’ll be cited as late because it does not trigger the necessary condition?
what if, during the test, i did saw an answer like the example, "Kumar arrived 17 minutes late then the last bell rang", but the rule was "student will be cited late only if they arrive 5 minutes after the last bell rang", then kumar answer choice will be the wrong answer (he's not late), only because the condiition said "only if"? (which in the real world, he should be consume as late?)
I thought the Kumar example was wrong only because I didn't want to assume that Kumar was even a student, haha. I was like, what if he's the teacher?? Yeah..i'm overthinking.
When I was in high school, in the morning, the school security guard would stand at the school gate to confiscate student IDs from anyone who was late when the homeroom bell rang. Those students were penalized for being late and had to serve detention. However, after about 10 minutes, the security guard had to go to the back of the school to help raise the American flag, and no one was present at the gate to penalize students who were late after that.
I thought of the Kumar example like this: since "only if" is a necessary indicator, then Kumar is in the superset. This means that he is not in the sufficient subset which would be indicated by "if". The subset here would be "students being cited as late". But since he is only in the superset, indicated by "only if", it is not explicitly known that he did in fact get cited.
For those who need some help with the Kumar example, it’s not a valid argument because it runs counter to the logical flow. Just because Kumar is 17 minutes past the bell doesn’t necessarily mean he’ll be properly cited as late. He might have had a doctor’s appointment and was allowed to come to class tardy, meaning he will not be properly cited as late. Simply because he falls within the ‘5+ minutes’ superset doesn’t imply that he falls within the ‘late’ subset.
Can someone explain why Kumar isn't late? I have no clue how, when the rule states that if a student is more than 5 minutes late, then they will be cited as late, yet Kumar, who arrives 17 minutes late (more than 5), isn't cited as late. I see people's explanations revolving around the use of "only if," but I don't see how that changes the outcome. Thanks
Students are cited as 'late' only IF they arrive more than 5 minutes past the last ring of the homeroom bell
late --> 5 minutes
/5 minutes late --> /late
BUT
Students are cited as 'late' IF they arrive more than 5 minutes past the last ring of the homeroom bell
5 minutes late --> late
/late --> /5 minutes
Students are cited as 'late' ONLY IF (NECESSARY) they arrive more than 5 minutes past the last ring of the homeroom bell (necessary condition from ONLY IF)
late --> 5 minutes
Kumar arrived 17 minutes after the last ring of the homeroom bell.
Therefore, Kumar will be cited as "late". (sufficient condition)
5 minutes late (17 minutes after) --> Late (sufficient)
If you are just 5 minutes late, you are cited late.
BUT NOT THE SAME AS NECESSARY:
late ONLY IF they arrive more than 5 minutes
late --> 5 minutes after bell
In order to be cited late you ONLY must arrive 5 minutes after bell.
Being cited Late is a subset of 5 minutes after. Kumar will be in the superset (5 minutes after), but not in the subset (being cited as late).
So basically we're saying being 5+ late is necessary to be cited as late, but not sufficient by itself. You could be 17 minutes late but have a doctor's notice, so you wouldn't be marked late. I.e., it's necessary, but not sufficient.
I think the confusion comes from the idea of necessity which does not mean "the only valid reason."
Air is necessary for me to live, but not sufficient. I also need food and water. But if I'm alive, I know I have air. I could have had air but also be dead because I didn't get food or water.
So, if I'm understanding correctly... if the statement instead was "Students are cited as 'late' IF they arrive more than 5 minutes past the last ring of the homeroom bell," then this would read in lawgic as 5+ min late --> cited as late. And in that case, then Kumar would be cited as late? The "ONLY IF" is what places the statement following the 'only if' in the necessary vs the sufficient condition?
If I used it in my own example...
"If it is Sunday, I will go on a hike." Reads: Sunday --> Hike.
"Only if it is Sunday, I will go on a hike." Reads: Hike --> Sunday.
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!
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428 comments
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.
Let me see if I’m grasping this correctly… the example with Kumar arriving 17 minutes after the bell doesn’t allow us to conclude he’ll be cited as late because it does not trigger the necessary condition?
Thank god for comments. i was totally lost
what if, during the test, i did saw an answer like the example, "Kumar arrived 17 minutes late then the last bell rang", but the rule was "student will be cited late only if they arrive 5 minutes after the last bell rang", then kumar answer choice will be the wrong answer (he's not late), only because the condiition said "only if"? (which in the real world, he should be consume as late?)
I thought the Kumar example was wrong only because I didn't want to assume that Kumar was even a student, haha. I was like, what if he's the teacher?? Yeah..i'm overthinking.
What is confusing me with the Kumar example is that we have to assume there's this hypothetical scenario where he doesn't get cited as late... right?
After 20mins, I think I understand it now.
Statement: "You can go to law school only if you have a bachelor's degree"
Translation: Law school → Bachelor's degree
What this means:
Bachelor's degree is NECESSARY (required)
But bachelor's degree is NOT SUFFICIENT (not enough by itself)
You ALSO need: LSAT score, GPA, application, letters of rec, etc.
Question: "You have a bachelor's degree. Can you go to law school?"
Answer: We don't know! You have ONE necessary condition, but you need ALL of them (LSAT, GPA, etc.)
Vs.
Statement: "You can go to law school if you have a bachelor's degree"
Translation: Bachelor's degree → Law school
What this means logically:
Bachelor's degree is SUFFICIENT (enough by itself)
Having a bachelor's degree GUARANTEES law school admission
LSAT doesn't matter, GPA doesn't matter, nothing else matters. You have any bachelors, congrats you get in!
Question: "You have a bachelor's degree. Can you go to law school?"
Answer: Yes!
When I was in high school, in the morning, the school security guard would stand at the school gate to confiscate student IDs from anyone who was late when the homeroom bell rang. Those students were penalized for being late and had to serve detention. However, after about 10 minutes, the security guard had to go to the back of the school to help raise the American flag, and no one was present at the gate to penalize students who were late after that.
I thought of the Kumar example like this: since "only if" is a necessary indicator, then Kumar is in the superset. This means that he is not in the sufficient subset which would be indicated by "if". The subset here would be "students being cited as late". But since he is only in the superset, indicated by "only if", it is not explicitly known that he did in fact get cited.
For those who need some help with the Kumar example, it’s not a valid argument because it runs counter to the logical flow. Just because Kumar is 17 minutes past the bell doesn’t necessarily mean he’ll be properly cited as late. He might have had a doctor’s appointment and was allowed to come to class tardy, meaning he will not be properly cited as late. Simply because he falls within the ‘5+ minutes’ superset doesn’t imply that he falls within the ‘late’ subset.
Can someone explain why Kumar isn't late? I have no clue how, when the rule states that if a student is more than 5 minutes late, then they will be cited as late, yet Kumar, who arrives 17 minutes late (more than 5), isn't cited as late. I see people's explanations revolving around the use of "only if," but I don't see how that changes the outcome. Thanks
Haha he's talking so fast he's locked in
Had a lot of issues with this but after a while I got it.
"ONLY IF" → required, not guaranteed → may
"IF" → guaranteed → must
Students are cited as 'late' only IF they arrive more than 5 minutes past the last ring of the homeroom bell
late --> 5 minutes
/5 minutes late --> /late
BUT
Students are cited as 'late' IF they arrive more than 5 minutes past the last ring of the homeroom bell
5 minutes late --> late
/late --> /5 minutes
Students are cited as 'late' ONLY IF (NECESSARY) they arrive more than 5 minutes past the last ring of the homeroom bell (necessary condition from ONLY IF)
late --> 5 minutes
Kumar arrived 17 minutes after the last ring of the homeroom bell.
Therefore, Kumar will be cited as "late". (sufficient condition)
5 minutes late (17 minutes after) --> Late (sufficient)
If you are just 5 minutes late, you are cited late.
BUT NOT THE SAME AS NECESSARY:
late ONLY IF they arrive more than 5 minutes
late --> 5 minutes after bell
In order to be cited late you ONLY must arrive 5 minutes after bell.
Being cited Late is a subset of 5 minutes after. Kumar will be in the superset (5 minutes after), but not in the subset (being cited as late).
I will go on a hike, if it is Sunday.
Sunday --> Hike
/Hike --> /Sunday
Omar woke up on Sunday.
Therefore, Omar will go on a hike.
Sunday --> Hike
Conclusion. Valid.
BUT
I will go on a hike, ONLY if it is Sunday.
Hike --> Sunday
Omar woke up on Sunday.
Therefore, Omar will go on a Hike.
Sunday --> Hike
Conclusion. INVALID.
So basically we're saying being 5+ late is necessary to be cited as late, but not sufficient by itself. You could be 17 minutes late but have a doctor's notice, so you wouldn't be marked late. I.e., it's necessary, but not sufficient.
I think the confusion comes from the idea of necessity which does not mean "the only valid reason."
Air is necessary for me to live, but not sufficient. I also need food and water. But if I'm alive, I know I have air. I could have had air but also be dead because I didn't get food or water.
Is my logic sound?
So, if I'm understanding correctly... if the statement instead was "Students are cited as 'late' IF they arrive more than 5 minutes past the last ring of the homeroom bell," then this would read in lawgic as 5+ min late --> cited as late. And in that case, then Kumar would be cited as late? The "ONLY IF" is what places the statement following the 'only if' in the necessary vs the sufficient condition?
If I used it in my own example...
"If it is Sunday, I will go on a hike." Reads: Sunday --> Hike.
"Only if it is Sunday, I will go on a hike." Reads: Hike --> Sunday.
??
hey i don't understand why kumar isn't late while the stimulus stated "more than five minutes"?
I drew the conclusion that it would be invalid if Kuman arrived late because it is not implied that he is a "student." Would that be invalid?
so the kumar example is logically invalid and untruthful but LAWGICly valid
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!