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.
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.
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.
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
Had a lot of issues with this but after a while I got it.
"ONLY IF" → required, not guaranteed → may
"IF" → guaranteed → must
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450 comments
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?
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.
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?
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....
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!!
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