Ok so I THINK I am starting to understand this. Basically a necessary condition to be cited as late is that you must be more than 5 minutes late. But just because you are 5+ minutes late doesn’t guarantee that you are cited as late because there could other factors like, idk be excused or maybe the teacher forgot to cite them.
But, if someone was was cited late, that is sufficient to say they were 5+ minutes late because it is necessary to be 5+ minutes late to be cited as late.
So lets say:
Students are cited as "late" only if they arrive more than five minutes past the last ring. Melissa arrived less than five minutes past the last ring. Therefore, Melissa cannot be cited as "late."
We know for a fact that Melissa cannot be cited as late because they did not come 5+ minutes late. But:
Students are cited as "late" only if they arrive more than five minutes past the last ring. Kumar arrived 17 minutes after the bell. Therefore, Kumar MAY be cited as late.
So basically now that Kumar is 17 minutes late, there is a possibility to be marked as late because to be marked as late, it is necessary to be 5+ minutes late. But being 17 minutes late does not guarantee a late citation.
Can anyone verify or correct my thought process please? Thank you in advance!
Thank you for explaining this because your explanation made me better understand this concept!! It sounds right to me, but I'm also learning this so not 100% sure.
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.
Okay, the Kumar example broke my brain at first, but I worked it out on paper and I want to share my thought process in case it helps anyone else.
-------------------------------------
First, let's break down the problem.
Sufficient Condition = being cited as late
important to note that we are talking about being cited as late, not just being late
Necessary Condition = arriving more than 5 minutes past the last ring of the homeroom bell.
[Late --> 5+]
-------------------------------------
I then had to go back to understand If vs Only If theory in super basic terms.
IF indicates the Sufficient Condition. This means that the First Event's occurrence guarantees the Second Event's occurrence.
Ex. If one is a cat [Sufficient Condition] then one is a mammal [Necessary Condition].
Being a cat guarantees being a mammal. It is not possible for one to be a cat without also being a mammal.
ONLY IF indicates the Necessary Condition, meaning that the Second Event's occurrence is required for the First Event's occurrence to be possible.
The occurrence of the Second Event [the Necessary Condition] does NOT GUARANTEE the occurrence of the First Event [the Sufficient Condition].
Ex. If one is a mammal, one is a cat.
[^^^^ This does not make sense. The Necessary Condition (being a mammal) does not guarantee the Sufficient Condition (being a cat). One could be a mammal, and not be a cat.]
What really helped me to understand this aspect of the Necessary Condition is that the Necessary Condition is what makes all Sufficient Conditions possible, but it does not guarantee any particular Specific Condition.
For example, being a mammal means one could be a cat, dog, horse, etc. Being a mammal does not guarantee that one is specifically a cat or specifically a dog or specifically a horse.
-------------------------------------
Okay, so back to the Kumar example.
First, I translated the symbolic logic of [Late --> 5+] back into English using the (if A --> then B) format.
"If a student is cited as 'late,' [Sufficient Condition] then they arrived more than five minutes past the last ring of the homeroom bell [Necessary Condition]."
This makes sense, the occurrence of the First Even [Sufficient Condition] guarantees the occurrence of the Second Event [Necessary Condition].
For a student to be cited as 'late' it is guaranteed that they arrived more than 5 minutes past the last ring of the homeroom bell. If a student did not arrive more than 5 minutes past the last ring of the homeroom bell, they would not be cited as late.
But, if we try to switch things around [like I did above with the cat and mammal example] things start to get wonky and do not work.
If a student arrived more than five minutes past the last ring of the homeroom bell [Necessary Condition], then the student is cited as "late." [Sufficient Condition]
This statement is not valid because the Necessary Condition does not guarantee the Sufficient Condition.
The same way that being a mammal does not guarantee being a cat, the behavior of showing up more than 5 minutes past the final ring of the homeroom bell does not guarantee being cited as late. It makes being cited as late a possibility, but it does not guarantee that that event will occur, because there are also many other possibilities that could happen.
I think part of the reason that I struggled so much to wrap my head around this is
I confused being "cited as late" with "being late" -- these are 2 very different things!
My confusion between "being late" and "being cited" stopped me from understanding the other possibilities of what could happen to Kumar.
The same way that being a mammal opens the possibility for being a cat, whilst also opening the possibility for being a dog, horse, etc.
Kumar being 17 minutes late opens the possibility for him to be 'cited as late' but it also opens the possibility for him to be given a warning, be given detention, for his teacher not to notice and nothing to happen, etc.
-------------------------------------
Anyways I know this was very long winded and repetitive, but it was only through thinking out the example in this in-depth way that I was able to understand where I originally went wrong :)
@jordkerns I feel dumb because I still don't understand why Kumar is not being cited as late.
Is it because the question is "can you draw a valid conclusion that therefore Kumar will be cited as late?". So I'm not being asked to assess the rules of the logic here, but rather we're being asked if Kumar being cited as late is a definite.
I'm still lost because it feels like we're going above and beyond by injecting our own interpretations here, "maybe the staff just didn't feel he deserved a negative citation," and such. And I'm struggling when and where to exercise similar interpretations.
You are being asked to assess the rules of logic. The fact that the Necessary Condition does not guarantee the Sufficient Condition is one of the most basic and most important rules of logic.
Just because Kumar is more than 5 minutes past the final bell, does not guarantee that he will be issued a late citation -- because of the logical rule that the Necessary Condition does not guarantee the Sufficient Condition.
For me, using hypotheticals of the other things that could happen to Kumar (no one notices, he gets a warning, he had a hall pass, whatever) help me to see why the Necessary Condition does not guarantee the Sufficient Condition, because it shows me some of the other possible Sufficient Conditions that could exist in a valid logical relationship with the Necessary Condition.
However, if that is unhelpful to you -- then don't do it. Just use the rules of logic. We know that the Necessary Condition is being 5+ minutes late after the final bell. We know that the Sufficient Condition is being cited as late.
Therefore, we know, using the rules of logic, that Kumar being 5+ minutes late CANNOT guarantee that he was cited as late. Why? Because the Necessary Condition CANNOT guarantee the Sufficient Condition. The Necessary Condition makes all Sufficient Conditions possible, but does not guarantee any specific one.
If I were you I would do a lot more study on Necessary vs Sufficient conditions until you understand that concept backwards and forwards. The dog and mammal example that I used in my first response can be helpful.
Not sure how else to explain this, but hopefully it is more clear now.
@jordkerns the last part helped me EXTREMELY. Being "cited" as late does not mean Kumar WAS late. He could have snuck into first period without being caught so he did not NECESSARILY get cited as "late". (thank you so much)
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.
I'm writing this for myself to wrap my head around it, but I hope it might help someone else as well.
"A cat eats lasagna only if their owner is home"
"the cat's owner is home"
"therefore, the cat eats lasagna" wrong conclusion
eats lasagna -> owner home
/ owner home -> / eat lasagna
The conclusion here is wrong because just because the owner is home doesn't mean the cat has to eat lasagna. It could also eat a brownie or cat food when the owner is home. But for the cat to eat lasagna the owner has to be home.
So, just because something is necessary for something to be true, does not mean it is true if the condition(s) are met.
For me this example is a little less confusing than the Kumar example.
Yes, but conclusions don't usually end that way. The authors usually throw in assumptions or invalid forms of reasoning that they want the students to identify. Typically, it would be the conclusion the writer wrote initially, or a 'could be' statement that lessens the degree.
Another way I'm thinking of this to help me understand the Kumar situation is like this:
One can be considered a cat only if they are a part of the mammal animal family. Bob is a mammal.
Does this mean Bob is a cat? No, not necessarily. Because he's a mammal, he has a chance at being a cat, but we don't know whether he is a cat or not. We just know that because Bob has fulfilled the necessary condition (being a mammal), he is in the running for maybe being a cat (sufficient condition). He could be a dog, human, rabbit, etc. Who knows. All we know is that Bob is a mammal, so there's a chance that he could be a cat. If Bob was a chair, there's no chance he could be a cat - because he hasn't fulfilled the necessary condition of being a mammal.
Now let's apply this to Kumar.
Students can be* cited as "late" only if they arrive more than five minutes past the last ring of the homeroom bell. Kumar arrived 17 minutes late.
Does this mean Kumar is cited as late? No, not necessarily. Because he arrived 17 minutes late, he has a chance at being cited late, but we don't know whether he has been cited late or not. We just know that because Kumar has fulfilled the necessary condition (arriving more than 5 min. late), he is in the running for maybe being cited late (sufficient condition). Say he arrived 16 min late, 15 min late, 14 min late, etc. - as long as he arrived more than 5 minutes late, there's a chance he could be cited.
*changed the original "are" to "can be" for clarity
Let me know if I've got this wrong, but thinking of it this way made the official explanation make more sense to me.
took me a little bit to figure this out, because the kumar example confused me inititally, so I wanna explain in my comment in case it helps anyone else out to think of it like this:
-we just learned the indicators for /necessary/ conditions, so we know that "only if" indicates that "arriving more than 5 min past the bell" is a necessary condition
-we are told that kumar arrived 17 min past the bell, and intuitively we want to assume that he must be late
but remember: sufficient -> necessary
-if i am a cat, that is sufficient to know that i am a mammal. but if i am a mammal, that does not necessarily mean i am a cat.
the same applies to this argument
-if i am late, than it is sufficient to know that i arrived 5+ min past the bell. but arriving 5+ min after the bell does not necessarily mean i am late.
-think about it like this-- kumar arrived 17 min past the bell, but there's many reasons he could possibly not been late: he could have just not gotten caught, or maybe had an excuse so he didn't get written up, etcetc...we don't know!
but from the information we've been told, we aren't able to make the assumption that he's late
I still question Kumar's lateness as no when we are to stick to the information provided only. There's nothing indicating in the necessary condition that Kumar's 17 minutes late should meet the 5+ minutes late as a citation especially if its a necessary condition. JY can you give some input on the difference without any outside assumptions as to why Kumar is cited late and Elias not being cited as late when he met the 5+ necessary condition
I mean Kumar is cited as not being late while Elias is cited as being late. I reviewed the other comments regarding sufficient and necessary conditions but I'm still not getting a good grasp without inferences as to why both are not considered late. Please advise. Thanks
Might be worth acknowledging an important nuance in your logic and explanation.
"You can go to law school only if you have a bachelor's degree"
Can go Law school > Have Bachelors
Actually leaves the possibility open to attending law school with JUST a bachelors. It is not guaranteed, but it is a possibility. In the world of your claim, it could be true that you get to go to law school with just a BS. It is not sufficient, which means it is not guaranteed, but it's possible, regardless of the added detail in your explanation. Your claim has nothing to do with all the other needs we know are required for law school.
I think the Kumar example is just confusing because it can be applied so easily to real world setting and your brain jumps to "but he is late! he will be cited!" For the purpose of LSAT we're all expected to ignore what we already know and just focus on the text.
Like for me it helped to change the example to "a person can leave Disney World only if they punch Mickey Mouse in the guts" IMO the more ridiculous the better. Here the necessary condition is "punch Mickey" and sufficient condition is "leave Disney World" right? Now consider the phrase "Kumar punched Mickey Mouse in the guts." Do we have enough info to infer that Kumar has left Disney World? The answer would be no; we know that Kumar CAN leave Disney World now (=he has fulfilled necessary condition), but we don't know if he DID leave or not (sufficient condition).
Now if the original phrasing was "a person leaves Disney World if they punch Mickey Mouse in the guts" Kumar punching Mickey automatically means that he left Disney.
Hope this helps because this was tripping me up for a while!
Honestly, this made no sense to me before, but once I compared it to another example that we have done before it made more sense.
The example I used was "If one is a cat, then one is a mammal." So from past lessons, we learned that "If one is a cat" is the sufficient condition, and "then one is a mammal" is the necessary condition. In other words, being a cat is sufficient (good enough) information to assume that one is a mammal. (Which can be lawgically represented as C → M). However, if you went the other way (if you lawgically do C ← M [which can be read "if one is a mammal then one is a cat"]) this statement would not be accurate. That's because knowing something is a mammal is not sufficient (good enough) information to assume that they are a cat (and in this case that makes sense right? Like there are plenty of other mammals that are not cats.)
Therefore, using that same lawgic can help with the Kumar example. The example says: Students are cited as "late" only if they arrive more than five minutes past the last ring of the homeroom bell. For this example, "Students are cited as late" is the sufficient (good enough) condition, and "arriving more than five minutes late" is the necessary condition (Which can lawgically be represented as Cited Late → 5+). However, again here if you went the other way (that is, if you lawgically do Cited Late ← 5+ [which can be read "if one is arrives more than 5 minutes after the bell, then one is cited as late]) this statement would not be accurate. That's because knowing that someone arrived 5 minutes after school starts is NOT sufficient (good enough) information to assume that they were cited as late. This also makes sense if you think of it too, there are plenty of reasons that Kumar, who arrived 17 minutes late, did not get cited as late... for example, he could have been excused, or he could have had a chill teacher who just didn't care.
Anyways that's what helped me most because I was really confused about this one until I started comparing it to others that made more sense to me. Another thing I did was change the indicator... Instead of saying "Only if" I used "only when" because Idky but that just made more sense to me.
Hope this helps, and feel free to correct me if I am wrong in any way!
I'm just here to throw in another simplified example that shares the characteristic of the Kumar example.
You can eat strawberries every day only if you have strawberries.
Jenna has strawberries.
Therefore, Jenna eats strawberries every day.
This does not mean Jenna eats strawberries every day. It simply states that if you have strawberries (the necessary condition), then you can eat them every day (the sufficient condition).
@CamilleChmura I just want to note that adding "Therefore, Jenna eats strawberries every day" was to illustrate the same mistake as "Therefore, Kumar will be cited as late."
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.
All I know is: He meets the necessary condition for getting cited (he was late enough to be cited).
BUT...
The rule didn’t say: If you arrive 5+ mins late, you WILL be cited.
It only told me: You can’t be cited unless you were 5+ mins late. "only if they are more than 5+ min late", This is the only indicator that Kumar has for being cited but its not enough to get cited.
- The rule says: Students are cited as "late" only if they arrive more than five minutes late. This means arriving more than 5 minutes late is necessary for being cited as late. But arriving late alone doesn't guarantee that the student will be cited—other factors could be involved.
- So, Kumar arriving 17 minutes late fulfills the necessary condition (arriving more than 5 minutes late), but it does not guarantee he will be cited. We don’t have enough information to make that judgment.
- another example -
You can only enter a club if you're over 21 years old.
- Being over 21 is necessary to enter the club, but just being over 21 doesn't guarantee you'll get in. You might also need a membership, a reservation, or be dressed appropriately. So, being over 21 is necessary, but it’s not sufficient on its own to guarantee entry.
In the homeroom bell example:
Students are cited as "late" only if they arrive more than five minutes late.
- Arriving more than 5 minutes late is necessary for being cited as late, but it doesn't guarantee the student will be cited. Something else could also factor into the decision (like maybe the teacher lets it slide or there's an exception made).
Wait I think I'm confused with your language here. In your bar example, I circled "only" with the words following "enter a club" as the necessary conditions, while "if" and the words following "you're over 21 years old" are the sufficient conditions. Therefore "enter a club" is the superset and "+21" is the subset, wouldn't that make being + 21 sufficient to enter a club?
I think the club example is helpful in clarifying the relationship between the sufficient and necessary conditions. It is not always intuitive and takes some work, so thank you to all of you in the comments section for the helpful hints!
But what if we changed the bar example into 'you can go to a bar if you are over 21' (instead using 'only if') (or, is it wrong to rewrite in this way?)
Does it make 'go to a bar' sufficient? Emily is over 23. She is over 21, so she can go to a bar. But she can also go to places other than bar such as a nightclub, a court or some dangrous places with age limit. Being 21 is necessary for Emily to go to a bar but she does not have too go to a bar and hence she has other options.
Then we go back to the example: ' you can go to a bar only if you are over 21'
Emily can go to a bar. She must be over 21. But going to bar does not necessary make her to be over 21???????? I think I am still very confusing. Do I still make mistakes on differentiating the premise from conlcusion?????
yeah the first example "you can go to a bar if you are over 21" is perfect because you made being 21 sufficient (good enough to get into the bar). the statement is not saying that she has to go to the bar, or even that she will, but just that she CAN. you're right, she can go to other places and we don't know if she will or won't, we just know for certain that if the bar is on her agenda, she will be allowed to go because she satisfies the sufficient condition. if the sufficient condition is satisifed the necessary will occur. so if she is over 21 she can go to the bar.
the second one, "you can go to a bar only if you are over 21" is saying that if you enter the bar at all, you must be 21. there may be other things you need, we do not know, but being 21 is necessary. so if you go into a bar and see Emily, you know she's 21. for the contrapositive "if you are not over 21 you can not go to the bar" → if emily texts you and tells you it's her 20th birthday, you can say congratulations, but you can not invite her to the club because she will not get in. She does not satisfy the necessary condition.
Yeah I know this can be confusing because "if" and "only" on their own usually suggest different things. "If" typically signals a sufficient condition (e.g., "If it rains, the ground gets wet"—rain is enough for wet ground). But when combined as "only if," it means the condition is necessary (e.g., "You can vote only if you’re a citizen"—being a citizen is required to vote). But it's sometimes difficult to see the "only if" phrasing. In the example, "You can only enter a club if you’re over 21 years old," the focus is on what’s required—being over 21. Even though "if" is there, it’s part of "only if," making age a requirement. The words in between, "enter the club," don't change that.
A good way to see this is to rephrase it: "To enter the club, you must be over 21." This translation can help make it clear that being 21 is required (necessary), but it doesn’t guarantee entry (sufficiency).
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.
So like... if Elias arrived 17 minutes after the last bell, but he had a doctor's note or something. Some OTHER instance or possibility could be true in which he is arriving 5 minutes past the last bell but would not be considered late. In visual terms, he could be within the larger circle (more than 5 minutes after the bell), while not being in the smaller circle (cited as late).
@AidanW yeah this is my thought process too, I think its right. I am sorta visualizing the circles in my head as I read these to try and understand them.
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.
Kumar example stumped me! I confused BEING LATE with being CITED AS LATE. It took me 20 minutes to sort out what was going on in my head. The mistake I made was assuming a sufficient condition when there was not one. The condition I assumed was "If you are caught late you will be cited" and I assumed that Kumar was caught.
Being CITED as late is a sufficient condition for being more than 5 minutes LATE.
But being LATE is NOT a sufficient condition for being CITED as late.
You can be LATE and not get CITED for it.
But you can't be CITED for being late if you were never LATE in the first place.
An example that is more clear is this:
People are cited as "speeding" only if they are going 10 mph over the speed limit.
Sam was going 25 mph over the speed limit.
Therefore, Sam will get a speeding ticket.
Going 10mph over the speed limit is a necessary condition for getting a speeding ticket.
But, it is not a sufficient condition in getting a speeding ticket. We are not given a sufficient condition in this argument that would guarantee the conclusion that "Sam will get a speeding ticket". The flaw in the argument is that its author assumed that going 10mph over the speed limit would guarantee that Sam gets a speeding ticket. However, the only thing that can guarantee Sam getting a speeding ticket, is Sam getting a speeding ticket.
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.
549 comments
Ok so I THINK I am starting to understand this. Basically a necessary condition to be cited as late is that you must be more than 5 minutes late. But just because you are 5+ minutes late doesn’t guarantee that you are cited as late because there could other factors like, idk be excused or maybe the teacher forgot to cite them.
But, if someone was was cited late, that is sufficient to say they were 5+ minutes late because it is necessary to be 5+ minutes late to be cited as late.
So lets say:
Students are cited as "late" only if they arrive more than five minutes past the last ring. Melissa arrived less than five minutes past the last ring. Therefore, Melissa cannot be cited as "late."
We know for a fact that Melissa cannot be cited as late because they did not come 5+ minutes late. But:
Students are cited as "late" only if they arrive more than five minutes past the last ring. Kumar arrived 17 minutes after the bell. Therefore, Kumar MAY be cited as late.
So basically now that Kumar is 17 minutes late, there is a possibility to be marked as late because to be marked as late, it is necessary to be 5+ minutes late. But being 17 minutes late does not guarantee a late citation.
Can anyone verify or correct my thought process please? Thank you in advance!
this is so well broken down, thank you!
Thank you for explaining this because your explanation made me better understand this concept!! It sounds right to me, but I'm also learning this so not 100% sure.
This is better than the original explanation!
This actually makes a lot of sense. You're a lifesaver thank you
@arrah203 Kumar could be cited absent!
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.
@RazanTadros Goat Explanation!
Okay, the Kumar example broke my brain at first, but I worked it out on paper and I want to share my thought process in case it helps anyone else.
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First, let's break down the problem.
Sufficient Condition = being cited as late
Necessary Condition = arriving more than 5 minutes past the last ring of the homeroom bell.
[Late --> 5+]
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I then had to go back to understand If vs Only If theory in super basic terms.
IF indicates the Sufficient Condition. This means that the First Event's occurrence guarantees the Second Event's occurrence.
Ex. If one is a cat [Sufficient Condition] then one is a mammal [Necessary Condition].
Being a cat guarantees being a mammal. It is not possible for one to be a cat without also being a mammal.
ONLY IF indicates the Necessary Condition, meaning that the Second Event's occurrence is required for the First Event's occurrence to be possible.
The occurrence of the Second Event [the Necessary Condition] does NOT GUARANTEE the occurrence of the First Event [the Sufficient Condition].
Ex. If one is a mammal, one is a cat.
[^^^^ This does not make sense. The Necessary Condition (being a mammal) does not guarantee the Sufficient Condition (being a cat). One could be a mammal, and not be a cat.]
What really helped me to understand this aspect of the Necessary Condition is that the Necessary Condition is what makes all Sufficient Conditions possible, but it does not guarantee any particular Specific Condition.
For example, being a mammal means one could be a cat, dog, horse, etc. Being a mammal does not guarantee that one is specifically a cat or specifically a dog or specifically a horse.
-------------------------------------
Okay, so back to the Kumar example.
First, I translated the symbolic logic of [Late --> 5+] back into English using the (if A --> then B) format.
"If a student is cited as 'late,' [Sufficient Condition] then they arrived more than five minutes past the last ring of the homeroom bell [Necessary Condition]."
This makes sense, the occurrence of the First Even [Sufficient Condition] guarantees the occurrence of the Second Event [Necessary Condition].
For a student to be cited as 'late' it is guaranteed that they arrived more than 5 minutes past the last ring of the homeroom bell. If a student did not arrive more than 5 minutes past the last ring of the homeroom bell, they would not be cited as late.
But, if we try to switch things around [like I did above with the cat and mammal example] things start to get wonky and do not work.
If a student arrived more than five minutes past the last ring of the homeroom bell [Necessary Condition], then the student is cited as "late." [Sufficient Condition]
This statement is not valid because the Necessary Condition does not guarantee the Sufficient Condition.
The same way that being a mammal does not guarantee being a cat, the behavior of showing up more than 5 minutes past the final ring of the homeroom bell does not guarantee being cited as late. It makes being cited as late a possibility, but it does not guarantee that that event will occur, because there are also many other possibilities that could happen.
I think part of the reason that I struggled so much to wrap my head around this is
I confused being "cited as late" with "being late" -- these are 2 very different things!
My confusion between "being late" and "being cited" stopped me from understanding the other possibilities of what could happen to Kumar.
The same way that being a mammal opens the possibility for being a cat, whilst also opening the possibility for being a dog, horse, etc.
Kumar being 17 minutes late opens the possibility for him to be 'cited as late' but it also opens the possibility for him to be given a warning, be given detention, for his teacher not to notice and nothing to happen, etc.
-------------------------------------
Anyways I know this was very long winded and repetitive, but it was only through thinking out the example in this in-depth way that I was able to understand where I originally went wrong :)
@jordkerns Nicely done
@jordkerns Very helpful assessment ! Thanks!
@jordkerns This is great!
@jordkerns I feel dumb because I still don't understand why Kumar is not being cited as late.
Is it because the question is "can you draw a valid conclusion that therefore Kumar will be cited as late?". So I'm not being asked to assess the rules of the logic here, but rather we're being asked if Kumar being cited as late is a definite.
I'm still lost because it feels like we're going above and beyond by injecting our own interpretations here, "maybe the staff just didn't feel he deserved a negative citation," and such. And I'm struggling when and where to exercise similar interpretations.
@BobbyJohn
You are being asked to assess the rules of logic. The fact that the Necessary Condition does not guarantee the Sufficient Condition is one of the most basic and most important rules of logic.
Just because Kumar is more than 5 minutes past the final bell, does not guarantee that he will be issued a late citation -- because of the logical rule that the Necessary Condition does not guarantee the Sufficient Condition.
For me, using hypotheticals of the other things that could happen to Kumar (no one notices, he gets a warning, he had a hall pass, whatever) help me to see why the Necessary Condition does not guarantee the Sufficient Condition, because it shows me some of the other possible Sufficient Conditions that could exist in a valid logical relationship with the Necessary Condition.
However, if that is unhelpful to you -- then don't do it. Just use the rules of logic. We know that the Necessary Condition is being 5+ minutes late after the final bell. We know that the Sufficient Condition is being cited as late.
Therefore, we know, using the rules of logic, that Kumar being 5+ minutes late CANNOT guarantee that he was cited as late. Why? Because the Necessary Condition CANNOT guarantee the Sufficient Condition. The Necessary Condition makes all Sufficient Conditions possible, but does not guarantee any specific one.
If I were you I would do a lot more study on Necessary vs Sufficient conditions until you understand that concept backwards and forwards. The dog and mammal example that I used in my first response can be helpful.
Not sure how else to explain this, but hopefully it is more clear now.
@jordkerns you ate up this explanation thank u <
@jordkerns the last part helped me EXTREMELY. Being "cited" as late does not mean Kumar WAS late. He could have snuck into first period without being caught so he did not NECESSARILY get cited as "late". (thank you so much)
Im so cooked
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.
@ColeCavanaugh Thank you king. This helped me a bunch
@ColeCavanaugh thank you THIS really helped
I'm writing this for myself to wrap my head around it, but I hope it might help someone else as well.
"A cat eats lasagna only if their owner is home"
"the cat's owner is home"
"therefore, the cat eats lasagna" wrong conclusion
eats lasagna -> owner home
/ owner home -> / eat lasagna
The conclusion here is wrong because just because the owner is home doesn't mean the cat has to eat lasagna. It could also eat a brownie or cat food when the owner is home. But for the cat to eat lasagna the owner has to be home.
So, just because something is necessary for something to be true, does not mean it is true if the condition(s) are met.
For me this example is a little less confusing than the Kumar example.
Thank you! This is so helpful
Thank you!
Would the correct conclusion be that the cat's owner is home, rather than him eating lasagna?
Thank you so much! I was so confused! This really helped!
Thank you!
Thank you for this! Definitely helpful
Yes, but conclusions don't usually end that way. The authors usually throw in assumptions or invalid forms of reasoning that they want the students to identify. Typically, it would be the conclusion the writer wrote initially, or a 'could be' statement that lessens the degree.
Another way I'm thinking of this to help me understand the Kumar situation is like this:
One can be considered a cat only if they are a part of the mammal animal family. Bob is a mammal.
Does this mean Bob is a cat? No, not necessarily. Because he's a mammal, he has a chance at being a cat, but we don't know whether he is a cat or not. We just know that because Bob has fulfilled the necessary condition (being a mammal), he is in the running for maybe being a cat (sufficient condition). He could be a dog, human, rabbit, etc. Who knows. All we know is that Bob is a mammal, so there's a chance that he could be a cat. If Bob was a chair, there's no chance he could be a cat - because he hasn't fulfilled the necessary condition of being a mammal.
Now let's apply this to Kumar.
Students can be* cited as "late" only if they arrive more than five minutes past the last ring of the homeroom bell. Kumar arrived 17 minutes late.
Does this mean Kumar is cited as late? No, not necessarily. Because he arrived 17 minutes late, he has a chance at being cited late, but we don't know whether he has been cited late or not. We just know that because Kumar has fulfilled the necessary condition (arriving more than 5 min. late), he is in the running for maybe being cited late (sufficient condition). Say he arrived 16 min late, 15 min late, 14 min late, etc. - as long as he arrived more than 5 minutes late, there's a chance he could be cited.
*changed the original "are" to "can be" for clarity
Let me know if I've got this wrong, but thinking of it this way made the official explanation make more sense to me.
This helped a lot, thank you!
thank you!! this was helpful<3
sooo helpful thank you!!
This was a perfect explanation. Thank You!!
This is exactly what I needed! Thank you!
THIS WAS SO HELPFUL!! Thank you!
They should use this as the example. So helpful.
@lpoturyan your explanation of 'Bob' is great -- major slay
I am so cooked after that Kumar one ngl...
took me a little bit to figure this out, because the kumar example confused me inititally, so I wanna explain in my comment in case it helps anyone else out to think of it like this:
-we just learned the indicators for /necessary/ conditions, so we know that "only if" indicates that "arriving more than 5 min past the bell" is a necessary condition
-we are told that kumar arrived 17 min past the bell, and intuitively we want to assume that he must be late
but remember: sufficient -> necessary
-if i am a cat, that is sufficient to know that i am a mammal. but if i am a mammal, that does not necessarily mean i am a cat.
the same applies to this argument
-if i am late, than it is sufficient to know that i arrived 5+ min past the bell. but arriving 5+ min after the bell does not necessarily mean i am late.
-think about it like this-- kumar arrived 17 min past the bell, but there's many reasons he could possibly not been late: he could have just not gotten caught, or maybe had an excuse so he didn't get written up, etcetc...we don't know!
but from the information we've been told, we aren't able to make the assumption that he's late
thank you this helped.
I still question Kumar's lateness as no when we are to stick to the information provided only. There's nothing indicating in the necessary condition that Kumar's 17 minutes late should meet the 5+ minutes late as a citation especially if its a necessary condition. JY can you give some input on the difference without any outside assumptions as to why Kumar is cited late and Elias not being cited as late when he met the 5+ necessary condition
That really did help, yes.
Contrapositives have been throwing me for a loop this entire time. I think I'm starting to finally get the concept enough to use it.
Thank you!
Thank you for explaining! Your break down did help me.
I mean Kumar is cited as not being late while Elias is cited as being late. I reviewed the other comments regarding sufficient and necessary conditions but I'm still not getting a good grasp without inferences as to why both are not considered late. Please advise. Thanks
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!
Might be worth acknowledging an important nuance in your logic and explanation.
"You can go to law school only if you have a bachelor's degree"
Can go Law school > Have Bachelors
Actually leaves the possibility open to attending law school with JUST a bachelors. It is not guaranteed, but it is a possibility. In the world of your claim, it could be true that you get to go to law school with just a BS. It is not sufficient, which means it is not guaranteed, but it's possible, regardless of the added detail in your explanation. Your claim has nothing to do with all the other needs we know are required for law school.
@JonathanKennedy22 this was super helpful!!
Ok I struggled with this one but then I thought of it this way:
You can make toast every day only if you have a toaster.
Bob has a toaster.
That doesn't necessarily mean Bob makes toast every day
This is the clearest explanation, thank you.
Very helpful!
I think the Kumar example is just confusing because it can be applied so easily to real world setting and your brain jumps to "but he is late! he will be cited!" For the purpose of LSAT we're all expected to ignore what we already know and just focus on the text.
Like for me it helped to change the example to "a person can leave Disney World only if they punch Mickey Mouse in the guts" IMO the more ridiculous the better. Here the necessary condition is "punch Mickey" and sufficient condition is "leave Disney World" right? Now consider the phrase "Kumar punched Mickey Mouse in the guts." Do we have enough info to infer that Kumar has left Disney World? The answer would be no; we know that Kumar CAN leave Disney World now (=he has fulfilled necessary condition), but we don't know if he DID leave or not (sufficient condition).
Now if the original phrasing was "a person leaves Disney World if they punch Mickey Mouse in the guts" Kumar punching Mickey automatically means that he left Disney.
Hope this helps because this was tripping me up for a while!
That was super helpful thanks!
you broke this down beautifully
well said, thank you!
Honestly, this made no sense to me before, but once I compared it to another example that we have done before it made more sense.
The example I used was "If one is a cat, then one is a mammal." So from past lessons, we learned that "If one is a cat" is the sufficient condition, and "then one is a mammal" is the necessary condition. In other words, being a cat is sufficient (good enough) information to assume that one is a mammal. (Which can be lawgically represented as C → M). However, if you went the other way (if you lawgically do C ← M [which can be read "if one is a mammal then one is a cat"]) this statement would not be accurate. That's because knowing something is a mammal is not sufficient (good enough) information to assume that they are a cat (and in this case that makes sense right? Like there are plenty of other mammals that are not cats.)
Therefore, using that same lawgic can help with the Kumar example. The example says: Students are cited as "late" only if they arrive more than five minutes past the last ring of the homeroom bell. For this example, "Students are cited as late" is the sufficient (good enough) condition, and "arriving more than five minutes late" is the necessary condition (Which can lawgically be represented as Cited Late → 5+). However, again here if you went the other way (that is, if you lawgically do Cited Late ← 5+ [which can be read "if one is arrives more than 5 minutes after the bell, then one is cited as late]) this statement would not be accurate. That's because knowing that someone arrived 5 minutes after school starts is NOT sufficient (good enough) information to assume that they were cited as late. This also makes sense if you think of it too, there are plenty of reasons that Kumar, who arrived 17 minutes late, did not get cited as late... for example, he could have been excused, or he could have had a chill teacher who just didn't care.
Anyways that's what helped me most because I was really confused about this one until I started comparing it to others that made more sense to me. Another thing I did was change the indicator... Instead of saying "Only if" I used "only when" because Idky but that just made more sense to me.
Hope this helps, and feel free to correct me if I am wrong in any way!
Thank you so much this really cleared it up for me!
I'm just here to throw in another simplified example that shares the characteristic of the Kumar example.
You can eat strawberries every day only if you have strawberries.
Jenna has strawberries.
Therefore, Jenna eats strawberries every day.
This does not mean Jenna eats strawberries every day. It simply states that if you have strawberries (the necessary condition), then you can eat them every day (the sufficient condition).
@CamilleChmura I just want to note that adding "Therefore, Jenna eats strawberries every day" was to illustrate the same mistake as "Therefore, Kumar will be cited as late."
@CamilleChmura Thanks for this!
@CamilleChmura incredibly helpful!! thank you
I feel dumb and will try again tomorrow. Kumar and I are not friends.
ty friends
We all go through it with the LSAT, keep your head up!
You are not alone. But lets keep pushing through.
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.
@Hanifa Thank you....LOL
@Hanifa Wow this helped haha thank you!!!!!!
@tst19 You're welcome :)
This helped me!!!
Kumar arrived 17 minutes late.
All I know is: He meets the necessary condition for getting cited (he was late enough to be cited).
BUT...
The rule didn’t say: If you arrive 5+ mins late, you WILL be cited.
It only told me: You can’t be cited unless you were 5+ mins late. "only if they are more than 5+ min late", This is the only indicator that Kumar has for being cited but its not enough to get cited.
Thanks! Helpful elaboration.
- The rule says: Students are cited as "late" only if they arrive more than five minutes late. This means arriving more than 5 minutes late is necessary for being cited as late. But arriving late alone doesn't guarantee that the student will be cited—other factors could be involved.
- So, Kumar arriving 17 minutes late fulfills the necessary condition (arriving more than 5 minutes late), but it does not guarantee he will be cited. We don’t have enough information to make that judgment.
- another example -
You can only enter a club if you're over 21 years old.
- Being over 21 is necessary to enter the club, but just being over 21 doesn't guarantee you'll get in. You might also need a membership, a reservation, or be dressed appropriately. So, being over 21 is necessary, but it’s not sufficient on its own to guarantee entry.
In the homeroom bell example:
Students are cited as "late" only if they arrive more than five minutes late.
- Arriving more than 5 minutes late is necessary for being cited as late, but it doesn't guarantee the student will be cited. Something else could also factor into the decision (like maybe the teacher lets it slide or there's an exception made).
Wait I think I'm confused with your language here. In your bar example, I circled "only" with the words following "enter a club" as the necessary conditions, while "if" and the words following "you're over 21 years old" are the sufficient conditions. Therefore "enter a club" is the superset and "+21" is the subset, wouldn't that make being + 21 sufficient to enter a club?
I think the club example is helpful in clarifying the relationship between the sufficient and necessary conditions. It is not always intuitive and takes some work, so thank you to all of you in the comments section for the helpful hints!
But what if we changed the bar example into 'you can go to a bar if you are over 21' (instead using 'only if') (or, is it wrong to rewrite in this way?)
Does it make 'go to a bar' sufficient? Emily is over 23. She is over 21, so she can go to a bar. But she can also go to places other than bar such as a nightclub, a court or some dangrous places with age limit. Being 21 is necessary for Emily to go to a bar but she does not have too go to a bar and hence she has other options.
Then we go back to the example: ' you can go to a bar only if you are over 21'
Emily can go to a bar. She must be over 21. But going to bar does not necessary make her to be over 21???????? I think I am still very confusing. Do I still make mistakes on differentiating the premise from conlcusion?????
Oh! Got it, so there can be distance between "only if." Thanks so much!
yeah the first example "you can go to a bar if you are over 21" is perfect because you made being 21 sufficient (good enough to get into the bar). the statement is not saying that she has to go to the bar, or even that she will, but just that she CAN. you're right, she can go to other places and we don't know if she will or won't, we just know for certain that if the bar is on her agenda, she will be allowed to go because she satisfies the sufficient condition. if the sufficient condition is satisifed the necessary will occur. so if she is over 21 she can go to the bar.
the second one, "you can go to a bar only if you are over 21" is saying that if you enter the bar at all, you must be 21. there may be other things you need, we do not know, but being 21 is necessary. so if you go into a bar and see Emily, you know she's 21. for the contrapositive "if you are not over 21 you can not go to the bar" → if emily texts you and tells you it's her 20th birthday, you can say congratulations, but you can not invite her to the club because she will not get in. She does not satisfy the necessary condition.
Yeah I know this can be confusing because "if" and "only" on their own usually suggest different things. "If" typically signals a sufficient condition (e.g., "If it rains, the ground gets wet"—rain is enough for wet ground). But when combined as "only if," it means the condition is necessary (e.g., "You can vote only if you’re a citizen"—being a citizen is required to vote). But it's sometimes difficult to see the "only if" phrasing. In the example, "You can only enter a club if you’re over 21 years old," the focus is on what’s required—being over 21. Even though "if" is there, it’s part of "only if," making age a requirement. The words in between, "enter the club," don't change that.
A good way to see this is to rephrase it: "To enter the club, you must be over 21." This translation can help make it clear that being 21 is required (necessary), but it doesn’t guarantee entry (sufficiency).
There's an option to invite people to study on analytics. I'll send you an invite!
Hi, I am looking for a study buddy as well. Can I join your crew?
I would love to join as well!:)
This was super helpful! Thank you!! I'm down for a study sess!
omg sure ive been looking for study buddies!
Same!
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!
@kadeleon thnx for this I was so lost
Thank god for comments. i was totally lost
So like... if Elias arrived 17 minutes after the last bell, but he had a doctor's note or something. Some OTHER instance or possibility could be true in which he is arriving 5 minutes past the last bell but would not be considered late. In visual terms, he could be within the larger circle (more than 5 minutes after the bell), while not being in the smaller circle (cited as late).
@AidanW yeah this is my thought process too, I think its right. I am sorta visualizing the circles in my head as I read these to try and understand them.
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.
Kumar example stumped me! I confused BEING LATE with being CITED AS LATE. It took me 20 minutes to sort out what was going on in my head. The mistake I made was assuming a sufficient condition when there was not one. The condition I assumed was "If you are caught late you will be cited" and I assumed that Kumar was caught.
Being CITED as late is a sufficient condition for being more than 5 minutes LATE.
But being LATE is NOT a sufficient condition for being CITED as late.
You can be LATE and not get CITED for it.
But you can't be CITED for being late if you were never LATE in the first place.
An example that is more clear is this:
People are cited as "speeding" only if they are going 10 mph over the speed limit.
Sam was going 25 mph over the speed limit.
Therefore, Sam will get a speeding ticket.
Going 10mph over the speed limit is a necessary condition for getting a speeding ticket.
But, it is not a sufficient condition in getting a speeding ticket. We are not given a sufficient condition in this argument that would guarantee the conclusion that "Sam will get a speeding ticket". The flaw in the argument is that its author assumed that going 10mph over the speed limit would guarantee that Sam gets a speeding ticket. However, the only thing that can guarantee Sam getting a speeding ticket, is Sam getting a speeding ticket.
ouchie head hurt
lol
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?
@william.l.dillon Great explanation