These examples would be much more helpful if they were kept in the same context. For example, if the sufficient condition were illustrated here using the “If the Chancellor's nefarious plan…” bit. That would allow the reader to compare them instead of trying to compare two different sentences while learning the concept.
While the explanations and examples are great, it would really help if there were just a couple of questions/exercises to practice at the end or after these lessons and the ones following this one. The practice lessons after the conditional indicator groups were great, something like that could work well with these? Though not as many lol.
Putting an example using negatives under the disjunction in the sufficient condition header added an unhelpful level of complexity. The content appears to describe that omitting either element of a sufficient disjunctive negates the possibility of triggering the necessary condition.
Small problem I think with the last example, the speaker interprets "If N or O are not adopted" as /N or /O, but I believe the more accurate translation would be /(N or O) because it seems to me that the statement says that it is not the case that N or O are adopted, which then would translate into /N and /O by demorgan's. I am sure I am making a mistake somewhere, but I have looked over the comments and the question many times and I cannot figure it out, any advice? #help
I’m thinking this too. /N or /O > /M would be “If either N or O is not adopted…” or “If N is not adopted, or O is not adopted…”
But it seems to me that “If N or O is not adopted” should be represented as you said, or as /N & /O > /M.
Example: “If I don’t shop or order takeout, I won’t have food for dinner.” I would have to neglect both shopping and ordering to miss out on dinner. Neglecting just one or the other would not be sufficient. I could miss shopping but still order. So…
/(Shop or Order) > /Dinner
Or
/Shop & /Order > /Dinner
But it wouldn’t follow to say
/Shop or /Order > /Dinner
To make the latter work, a better example would be “If I don’t have time to cook or I don’t have time to eat, I won’t be able to have dinner.” that would get:
/Cook or /Eat > /Dinner — if either one is negated, I miss out on my chance for dinner.
@IsaacNyberg I agree that English is ambiguous, and that both interpretations (the interpretation /N or /O and the interpretation /(N or O)) are valid interpretations in English. I take it that an unspoken message of this lesson is that the LSAT will use only the /N or /O interpretation unless context makes it very clear otherwise. The toy examples I came up with are as follows.
"If Nancy or Oliver is not adopted, then we will be sad that the one unadopted orphan has no family."
"We have adopted no gases for approved use in the laboratory and we will adopt zero or one gases today. The only gases we can adopt are Nitrogen or Oxygen. If Nitrogen or Oxygen is not adopted, then we will not have adopted a gas for use in the laboratory."
@ToweringTextbooks This link was useful to me: https://7sage.com/blog/why-is-or-so-confusing, which says "Context will tell you which meaning is intended and let me save you a lot of trouble and tell you right now that the meaning that the LSAT summons most often is 'and/or.'"
#help Just to clarify, is there any difference between the "or" being used in the sufficient in this example and the "or" we have classified in Group 3 (negate sufficient)?
Consider the use of "or" outside of being a sufficient or necessary condition:
"A or B."
That asserts that "A or B" is true. In other words, at least one of A or B (or both) is the case. We can translate this to "/A -> B" or "/B -> A" (Group 3). If A is not true, then B must be true. And, if B is not true, then A must be true.
But consider this statement, where "or" is used in the sufficient condition:
"If A or B --> C"
Here, the statement is not asserting that "A or B" must be true. It's saying that if at least one of A or B is true, then C must be true. But that doesn't mean that at least one of A or B actually has to be true. Remember -- it's entirely possible the sufficient condition doesn't trigger! Maybe neither A nor B are true? That's OK. The conditional rule just wouldn't tell us anything.
i don't understand why you can't split the arrow when there's a disjunction in the necessary condition. Is it because only one of the two can happen when the or is in the necessary condition?
@SaraMoreno let's say if it's a Friday, I'm going out or I'm going to bed early
F -> Out OR Early
if we split the arrow:
F -> going out
F -> going to bed early
this is incorrect, because it's saying if it's a Friday, both of those things MUST be true, whereas what the sentence is saying is it's one or the other
There could be a scenario where both could be true, let's say I go out early so I come home early. But it's a possibility and not a certainty, so that's why they're jointly necessary
@epayne17 me too and then I wonder if there's something I'm missing out on?? I watch these just to make sure I understand them from an English perspective but I never bothered learning to do the lawgic because of what you wrote. Hopefully that doesn't come back to bite me in the end
I think the "or" here is the same inclusive or as we learned in the conditional sentence. You can see this in the Palpatine example: if both Amidala AND the Jedi failed, it would still be consistent with the statement that either one of the two (Amidala or the Jedi) failed.
I'm a bit confused about how the second example shows that the sufficient condition is independent of each other but why doesn't the necessary condition on the first example also serve as independent of each other if only one is necessary?
In the first case, if the chancellor succeeds, we know FOR A FACT that one event will be triggered, the other event will triggered, or both can be triggered. The two events are thus RELATED to each other.
In the second case, we are setting ourselves up for failure. We are treating the two events as separate from each other when they are not; they are related to each other. We NEED one OR the other.
This is very different frame of mind when thinking of disjunction in sufficient conditions, where one event can trigger the other NO MATTER WHAT HAPPENED WITH THE OTHER EVENT.
It's hard to see now but when we have to answer "must be trues" this will make more sense.
I'm finding a parallel between Or and And statements in programming language. Hoping this will help me grasp this concept once things get more advanced lol
okay i get that or is independent on sufficient side and and is independent in necessary side and thus those two can split under given circumstances. However, I wonder how each would play out as often necessary condition becomes sufficient condition for other condition and vice versa.
Maybe I'm not understanding, but what is the point in splitting if its optional? JY mentions we can split, so why have a headache and not split at all? Any advice?
so if I am thinking correctly, I jotted down AF -> CS or JF -> CS, CS -> AF or JF. is that a correct way to look at it? i basically flipped the arrows in the video at 3 min
86 comments
OR in necessary = DON'T SPLIT
AND in necessary = You can split
OR in sufficient = You can split
AND in sufficient = DON'T SPLIT
(I hope this is right...correct me if needed)
These examples would be much more helpful if they were kept in the same context. For example, if the sufficient condition were illustrated here using the “If the Chancellor's nefarious plan…” bit. That would allow the reader to compare them instead of trying to compare two different sentences while learning the concept.
@matthewpfrye #feedback
While the explanations and examples are great, it would really help if there were just a couple of questions/exercises to practice at the end or after these lessons and the ones following this one. The practice lessons after the conditional indicator groups were great, something like that could work well with these? Though not as many lol.
#feedback
And: Can be split on the right side, but not on the left side.
Or: Can be split on the left side, but not on the right side.
#feedback please allow for the adjustment of the font size on closed captions! They take up so much space on the screen, it is distracting.
Putting an example using negatives under the disjunction in the sufficient condition header added an unhelpful level of complexity. The content appears to describe that omitting either element of a sufficient disjunctive negates the possibility of triggering the necessary condition.
wait yes absolutely, I am so confused by this too
Disjunction in the necessary condition:
If you like icecream, then you are a kid or you have a sweet tooth.
IC-> K or ST: one of the ideas in the necessary must be true. Both could be true but is not required.
Disjunction in the sufficient condition:
Don't make any noise or go out at night, the creatures will get you.
/N or /GO->Creatures: If you make noise the creatures will get you. Independently, if you go out at night the creatures will get you.
How do contrapositives work with these examples? My lawgic tells me that when we do the contrapositive, we can effectively change the or to an and?
For example
Plan Succeeds-> (Jedi Failed or Amidala Failed)
would become...
(Jedi and Amidala Succeeds) -> Plan fails
Are there caveats to this?
@Garrett_dom That's right! And what happens when you have and? "If A is true, then B and C are true."
The contrapositive of this would be:
If B is NOT true OR C is NOT true, then A is NOT true.
@BenPocheron haha
Small problem I think with the last example, the speaker interprets "If N or O are not adopted" as /N or /O, but I believe the more accurate translation would be /(N or O) because it seems to me that the statement says that it is not the case that N or O are adopted, which then would translate into /N and /O by demorgan's. I am sure I am making a mistake somewhere, but I have looked over the comments and the question many times and I cannot figure it out, any advice? #help
I’m thinking this too. /N or /O > /M would be “If either N or O is not adopted…” or “If N is not adopted, or O is not adopted…”
But it seems to me that “If N or O is not adopted” should be represented as you said, or as /N & /O > /M.
Example: “If I don’t shop or order takeout, I won’t have food for dinner.” I would have to neglect both shopping and ordering to miss out on dinner. Neglecting just one or the other would not be sufficient. I could miss shopping but still order. So…
/(Shop or Order) > /Dinner
Or
/Shop & /Order > /Dinner
But it wouldn’t follow to say
/Shop or /Order > /Dinner
To make the latter work, a better example would be “If I don’t have time to cook or I don’t have time to eat, I won’t be able to have dinner.” that would get:
/Cook or /Eat > /Dinner — if either one is negated, I miss out on my chance for dinner.
@IsaacNyberg I agree that English is ambiguous, and that both interpretations (the interpretation /N or /O and the interpretation /(N or O)) are valid interpretations in English. I take it that an unspoken message of this lesson is that the LSAT will use only the /N or /O interpretation unless context makes it very clear otherwise. The toy examples I came up with are as follows.
"If Nancy or Oliver is not adopted, then we will be sad that the one unadopted orphan has no family."
"We have adopted no gases for approved use in the laboratory and we will adopt zero or one gases today. The only gases we can adopt are Nitrogen or Oxygen. If Nitrogen or Oxygen is not adopted, then we will not have adopted a gas for use in the laboratory."
@ToweringTextbooks This link was useful to me: https://7sage.com/blog/why-is-or-so-confusing, which says "Context will tell you which meaning is intended and let me save you a lot of trouble and tell you right now that the meaning that the LSAT summons most often is 'and/or.'"
#help Just to clarify, is there any difference between the "or" being used in the sufficient in this example and the "or" we have classified in Group 3 (negate sufficient)?
Great question!
There is a difference.
Consider the use of "or" outside of being a sufficient or necessary condition:
"A or B."
That asserts that "A or B" is true. In other words, at least one of A or B (or both) is the case. We can translate this to "/A -> B" or "/B -> A" (Group 3). If A is not true, then B must be true. And, if B is not true, then A must be true.
But consider this statement, where "or" is used in the sufficient condition:
"If A or B --> C"
Here, the statement is not asserting that "A or B" must be true. It's saying that if at least one of A or B is true, then C must be true. But that doesn't mean that at least one of A or B actually has to be true. Remember -- it's entirely possible the sufficient condition doesn't trigger! Maybe neither A nor B are true? That's OK. The conditional rule just wouldn't tell us anything.
#help also wondering
Thank you!
'What happens if O is not adopted? Then M cannot be adopted, independent of what happens with M.'
Is 'M' supposed to be 'N' at the end of the second sentence?
I'm pretty sure it is!!
Yes you are correct. Both O and N most be adopted in order for M to be adopted.
While O and N don't affect one another, their outcomes affect M.
#help#feedback ^^
Disjunction in the necessary condition
To stay fit, you should run or hike.
fit → run or hike
At least one of the two ( run, hike ) is necessary.
Disjunction in the sufficient condition
If they want to buy a house or a car, they need a lot of money.
house or car → money
@Hanifa you repeated fit twice instead of adding hike in the necessary condition. But I appreciate the example, nonetheless.
The forums imo, is one of the best part of this website.
@MD_301Gopats Oh right, thanks for flagging that!! I just corrected it.
@MD_301Gopats
And yes, couldn't agree more! For me, the discussion section is where I find the answers to so many of my questions.
i don't understand why you can't split the arrow when there's a disjunction in the necessary condition. Is it because only one of the two can happen when the or is in the necessary condition?
@SaraMoreno let's say if it's a Friday, I'm going out or I'm going to bed early
F -> Out OR Early
if we split the arrow:
F -> going out
F -> going to bed early
this is incorrect, because it's saying if it's a Friday, both of those things MUST be true, whereas what the sentence is saying is it's one or the other
There could be a scenario where both could be true, let's say I go out early so I come home early. But it's a possibility and not a certainty, so that's why they're jointly necessary
So, if conjunction AND is in SC, we CANNOT split the arrow. If AND is in NC, we can split the arrow.
If disjunction OR is in SC, we can split the arrow. If OR is in NC, we CANNOT split the arrow.
does anyone else read these conjunction and disjunction lessons and think to themselves: "no shit"
@epayne17 me too and then I wonder if there's something I'm missing out on?? I watch these just to make sure I understand them from an English perspective but I never bothered learning to do the lawgic because of what you wrote. Hopefully that doesn't come back to bite me in the end
@iammichaelscott update .. it has
We learned before that (Or) in the LSAT means and/or = cloud be both but at least one.
So, why does (or ) here in conditions means (or) only??
I think the "or" here is the same inclusive or as we learned in the conditional sentence. You can see this in the Palpatine example: if both Amidala AND the Jedi failed, it would still be consistent with the statement that either one of the two (Amidala or the Jedi) failed.
#help
I'm a bit confused about how the second example shows that the sufficient condition is independent of each other but why doesn't the necessary condition on the first example also serve as independent of each other if only one is necessary?
CS → AF or JF
is fundamentally different in meaning from
CS-> AF
or
→JF
In the first case, if the chancellor succeeds, we know FOR A FACT that one event will be triggered, the other event will triggered, or both can be triggered. The two events are thus RELATED to each other.
In the second case, we are setting ourselves up for failure. We are treating the two events as separate from each other when they are not; they are related to each other. We NEED one OR the other.
This is very different frame of mind when thinking of disjunction in sufficient conditions, where one event can trigger the other NO MATTER WHAT HAPPENED WITH THE OTHER EVENT.
It's hard to see now but when we have to answer "must be trues" this will make more sense.
Shouldnt there be a parenthesis around "N or O" with the negation on the outside??
I'm finding a parallel between Or and And statements in programming language. Hoping this will help me grasp this concept once things get more advanced lol
okay i get that or is independent on sufficient side and and is independent in necessary side and thus those two can split under given circumstances. However, I wonder how each would play out as often necessary condition becomes sufficient condition for other condition and vice versa.
Maybe I'm not understanding, but what is the point in splitting if its optional? JY mentions we can split, so why have a headache and not split at all? Any advice?
If the Raptors escaped, either Nedry turned off the fences or the Raptors outsmarted the humans
RE-> NF or RoH
If Nedry turned off the fences or the Raptors outsmarted the humans, then the Raptors escaped
NF->
----------RE
RoH->
Right?
so if I am thinking correctly, I jotted down AF -> CS or JF -> CS, CS -> AF or JF. is that a correct way to look at it? i basically flipped the arrows in the video at 3 min
what would the contrapositive of this look like? If CF -> AF or JF, does that mean /AF AND /FJ -> /CF?