- if there’s an "and" in the sufficient condition:
Both parts of the "and" together are needed to trigger the outcome in the necessary condition. Neither part on its own is enough. So, keep the "and" together in the sufficient condition.
- if there’s an "and" in the necessary condition:
Each part of the "and" is required separately when the sufficient condition happens.
In Lawgic, this can be shown with separate statements, each connecting the sufficient condition to one of the necessary conditions.
Feels like sometimes the comment section explains the topic better than the videos, either way, thank you for the explanation and good luck on the lsat.
I get wanting to separate N and O because they are not related to each other, but that seems dangerous in practice. If M occurs, then BOTH N and O must occur. They are triggered by the same sufficient condition. I prefer to use parentheses to indicate that M is sufficient for both:
I thought through an example that shows how/why 2+ necessary conditions joined via conjunction are independently necessary, as the lesson states. Maybe it'll help:
Example statement: "I am happy only if my team wins and I score."
In lawgic: H → TW + IS, as "only if" is a Group 2, necessary condition indicator
The contrapositives would be:
/TW → /H, or more elaborately, /TW + IS → /H (Even if I do score, as long as the team loses, I am not happy)
/IS → /H, or more elaborately, TW + /IS → /H (Even if the team wins, if I do not score, I am not happy [selfish, lol!])
And together these both also imply, /TW + /IS → /H (If the team loses and I do not score, I'm definitely not happy)
So we can say the two necessary conditions are "independently necessary" overall, because as long as one fails in the contrapositive, then the sufficient condition also fails.
Quick, mostly pointless tip (aka the best kind); If you're the type to really want to shave seconds off your test time and dont want to have to type/write out a-n-d, you can use the humble Ampersand ('&', usually 7+Shift on the keyboard). its splitting hairs, but its slightly faster AND it looks cool 😎
I probably would keep the arrows on the same line to avoid confusion but one question I have if anyone can answer is wouldn't splitting on the necessary condition still indicate that one event could happen and not the other?
"M is adopted, then N and O are adopted."
Wouldn't splitting indicate that either N or O are adopted? When instead are trying to say that both have to be adopted?
@MRod Right, I'm confused about this also. I would think that both would have to be adopted because of the word "and". The word "Or" would mean that either one can happen, it doesn't need to be both.
@KhushyMandania i think of it as two overlapping supersets, with the subset being the intersection between the two. the subset can only exists in the intersection, so without it between in both, it cannot be in either.
For A + J -> CF, I thought of it as two overlapping subsets within the same superset, and the member being in the intersection of those two subsets, then the same applies.
@MRod I think the reason it is being broken apart is if you are trying to link to another premise such that says "if O happens then ...". Although the new premise doesn't explicitly say anything about N happening, you still know the new conditional relationship is triggered if M happens because M triggers both N and O.
from the review here can someone tell me if what i have bolded is correct?
If a conjunction occurs within the sufficient condition, both elements together guarantee the necessary condition. Neither alone is independently sufficient. In Lawgic, keep "and" within the sufficient condition. the two need each other to be necessary.
If a conjunction occurs within the necessary condition, two events are independently necessary when the sufficient condition is triggered. In Lawgic, these can be represented as separate conditionals leading from the sufficient condition. the two can both happen independent of another upon the sufficent.
how I understood it is that conjunction present in sufficient it means BOTH must be met to get the necessary. if conjunction present in the necessary to 2 ideas are independent from one another meaning if one is met so did the sufficient.
How important are these sections for the new LSAT format without logic games? I've noticed this entire section does not have videos, like the others.
Is this some correlation to the level of importance of the new LSAT structure? Or is it just purely coincidental? I am just trying to figure out where to focus most of my time. Thanks
i'm not sure if it's related to the new lsat structure; i think it's just meant to further our understanding of the notation and translating into logic which imo is applicable to the entire test. at the same time, i'm finding that a lot of these lessons without vids are pretty intuitive, so i don't take notes or anything and just read through quickly.
I'm not sure why, but I think I just got sufficient and necessary clarified in my head. When I used to explain it to myself, I had been confusing necessary for sufficient, thinking that necessary is what must happen for the sufficient rather than because the sufficient triggered it. I still get confused, but I'm glad I moved past that mental block LOL.
@Him Yes, not because O is not adopted but because we don't need O to be adopted to safely claim that N is adopted. The sufficient conditions "M is adopted" is enough.
@Edbnapa I'm pretty sure the lesson was on "or" (not and) being equivalent to and/or. This interpretation was only possible sometimes. The interpretation also depends on the context of the sentence.
@Igotthis123 Sorry that I don’t have an answer for you. I’m also wondering the same thing, so I am responding to be included in the response in case someone answers.
@Igotthis123 If you take the claim M is adopted as true it GUARANTEES that the N and O are both adopted. Given the lawgic form, M -> N and O, you can not just have M->N. The necessary clause is N and O are adopted.
Think of the NYC example. I could say, if one lives in NYC then they are Yankees fan and they live in the USA. Let's just take all these claims to be true and you end up with : NYC -> Yankees fan and live in USA
You would not say, if one lives in NYC then I know they are a Yankees fan, but I am not sure if they live in the USA. Based on the claims I established, one would have to be be both a yankees fan and live in the USA. Hope this helps.
I think you would only be able to make a valid conclusion for the contrapositive, so
A -> B and C
/B AND /C -> /A
/B = ?
/C = ?
/A = ?
if you only know that something is /B, you can't make a conclusion about what happens to C or A because we don't know. you only know that if its NOT B and NOT C then A doesn't happen.
So when the conjunction occurs within the necessary condition, like one or the other can be triggered? So, M--> O or M--> N or does it still need both to happen, but maybe not at the same time
@MarisolSanchezBoth will be triggered. M is sufficient to infer both N and O, so if M occurs, both N and O also occur. The conditional phrase mentioned nothing about time.
For the last bit, where the events in the necessary condition branch off, what does that imply about the temporality of the condition? Like, when M is adopted, that guarantees that N and O will be adopted. The branching path seems to say that when M is adopted, either N or O is adopted. Going down one path would seem to preclude the other. Rather the explanation here seems to say that both of those events can happen simultaneously. Is that true?
I can see where that comes from because of how it is displayed. I think try and think about it not as a branching (because you have to follow both arrows actually, you can't just choose one since they are both a result of M) but as a statement like M->O AND M->N meaning if M occurs, both O AND N occur.
79 comments
- if there’s an "and" in the sufficient condition:
Both parts of the "and" together are needed to trigger the outcome in the necessary condition. Neither part on its own is enough. So, keep the "and" together in the sufficient condition.
- if there’s an "and" in the necessary condition:
Each part of the "and" is required separately when the sufficient condition happens.
In Lawgic, this can be shown with separate statements, each connecting the sufficient condition to one of the necessary conditions.
Feels like sometimes the comment section explains the topic better than the videos, either way, thank you for the explanation and good luck on the lsat.
if i get a 180 everyone who responds to this I will take out for lunch.
@JamesVartian okok
@JamesVartian Sounds good to me.
@JamesVartian Guess I am not getting a free lunch...
@JamesVartian Do we get free lunch?
@JamesVartian Sounds great
@JamesVartian bet
I get wanting to separate N and O because they are not related to each other, but that seems dangerous in practice. If M occurs, then BOTH N and O must occur. They are triggered by the same sufficient condition. I prefer to use parentheses to indicate that M is sufficient for both:
M ---> ( N & O )
It's starting to click!
conjunction junction, what's your function?
I thought through an example that shows how/why 2+ necessary conditions joined via conjunction are independently necessary, as the lesson states. Maybe it'll help:
Example statement: "I am happy only if my team wins and I score."
In lawgic: H → TW + IS, as "only if" is a Group 2, necessary condition indicator
The contrapositives would be:
/TW → /H, or more elaborately, /TW + IS → /H (Even if I do score, as long as the team loses, I am not happy)
/IS → /H, or more elaborately, TW + /IS → /H (Even if the team wins, if I do not score, I am not happy [selfish, lol!])
And together these both also imply, /TW + /IS → /H (If the team loses and I do not score, I'm definitely not happy)
So we can say the two necessary conditions are "independently necessary" overall, because as long as one fails in the contrapositive, then the sufficient condition also fails.
Is this...right??
#feedback
Thank you! This helped.
Quick, mostly pointless tip (aka the best kind); If you're the type to really want to shave seconds off your test time and dont want to have to type/write out a-n-d, you can use the humble Ampersand ('&', usually 7+Shift on the keyboard). its splitting hairs, but its slightly faster AND it looks cool 😎
@ManusWeber hell yeah
@ManusWeber love this
I probably would keep the arrows on the same line to avoid confusion but one question I have if anyone can answer is wouldn't splitting on the necessary condition still indicate that one event could happen and not the other?
"M is adopted, then N and O are adopted."
Wouldn't splitting indicate that either N or O are adopted? When instead are trying to say that both have to be adopted?
@MRod #help this is exactly what I was thinking
@MRod Right, I'm confused about this also. I would think that both would have to be adopted because of the word "and". The word "Or" would mean that either one can happen, it doesn't need to be both.
@KhushyMandania i think of it as two overlapping supersets, with the subset being the intersection between the two. the subset can only exists in the intersection, so without it between in both, it cannot be in either.
For A + J -> CF, I thought of it as two overlapping subsets within the same superset, and the member being in the intersection of those two subsets, then the same applies.
@MRod I think the reason it is being broken apart is if you are trying to link to another premise such that says "if O happens then ...". Although the new premise doesn't explicitly say anything about N happening, you still know the new conditional relationship is triggered if M happens because M triggers both N and O.
from the review here can someone tell me if what i have bolded is correct?
If a conjunction occurs within the sufficient condition, both elements together guarantee the necessary condition. Neither alone is independently sufficient. In Lawgic, keep "and" within the sufficient condition. the two need each other to be necessary.
If a conjunction occurs within the necessary condition, two events are independently necessary when the sufficient condition is triggered. In Lawgic, these can be represented as separate conditionals leading from the sufficient condition. the two can both happen independent of another upon the sufficent.
@KayleeMurray so with #2, if sufficient is negated then both necessary conditions fail independently?
how I understood it is that conjunction present in sufficient it means BOTH must be met to get the necessary. if conjunction present in the necessary to 2 ideas are independent from one another meaning if one is met so did the sufficient.
pretty much both vs on or the other
I'm getting logic games flashbacks lolol
I think I prefer to use “+” as my symbol of choice when demonstrating the conjunction as it is quicker to write and understandable for me.
ex. A + J -> CF
Conjunction in the necessary condition:
CAT → mammal and animal
CAT → mammal
↘animal
Conjunction in the sufficient condition:
run + hike → active
We can NOT split the arrow in this case.
I think venn diagrams might be helpful to illustrate how this concept is applied.
How important are these sections for the new LSAT format without logic games? I've noticed this entire section does not have videos, like the others.
Is this some correlation to the level of importance of the new LSAT structure? Or is it just purely coincidental? I am just trying to figure out where to focus most of my time. Thanks
i'm not sure if it's related to the new lsat structure; i think it's just meant to further our understanding of the notation and translating into logic which imo is applicable to the entire test. at the same time, i'm finding that a lot of these lessons without vids are pretty intuitive, so i don't take notes or anything and just read through quickly.
Conjunction in the sufficient:
If Annie gets adopted and Mel gets adopted then Mrs. Hannigan will have no one to clean the orphanage.
A & M ->CO
Conjunction in the necessary:
If Mrs. Hannigan allows then the girls will have a dog and go to the movies.
H->D & M OR H->D, H->M
I'm not sure why, but I think I just got sufficient and necessary clarified in my head. When I used to explain it to myself, I had been confusing necessary for sufficient, thinking that necessary is what must happen for the sufficient rather than because the sufficient triggered it. I still get confused, but I'm glad I moved past that mental block LOL.
"If M is adopted, then N and O are adopted." Cant we say if M is adopted then N is adopted without saying and O?
@Him Yes, not because O is not adopted but because we don't need O to be adopted to safely claim that N is adopted. The sufficient conditions "M is adopted" is enough.
I am slightly confused because didn't we just have a lesson on "and" being equivalent to, "and/or"? Please inform me if I am misunderstanding!
@Edbnapa I'm pretty sure the lesson was on "or" (not and) being equivalent to and/or. This interpretation was only possible sometimes. The interpretation also depends on the context of the sentence.
So if we found out that M and N is adopted, is it safe to assume that O is also adopted?
@Igotthis123 Sorry that I don’t have an answer for you. I’m also wondering the same thing, so I am responding to be included in the response in case someone answers.
@Igotthis123 If you take the claim M is adopted as true it GUARANTEES that the N and O are both adopted. Given the lawgic form, M -> N and O, you can not just have M->N. The necessary clause is N and O are adopted.
Think of the NYC example. I could say, if one lives in NYC then they are Yankees fan and they live in the USA. Let's just take all these claims to be true and you end up with : NYC -> Yankees fan and live in USA
You would not say, if one lives in NYC then I know they are a Yankees fan, but I am not sure if they live in the USA. Based on the claims I established, one would have to be be both a yankees fan and live in the USA. Hope this helps.
@Igotthis123 yes, and you don't even need to know N is adopted, knowing M is adopted alone is sufficient to guarantee O is adopted.
@Igotthis123 Yes. Honestly you don't even need that much information to conclude that O is adopted; knowing M is adopted is sufficient.
@Igotthis123 I don't think so right, that would be going against the conditional arrow. N and O are necessary for M, but not sufficient.
How would you negate a statement like A -> B and C.
Lets say B does not happen, which makes it /B and allows us to contrapose back for /A. What happens to the C? Or, is this allowed?
Thanks #help
I think you would only be able to make a valid conclusion for the contrapositive, so
A -> B and C
/B AND /C -> /A
/B = ?
/C = ?
/A = ?
if you only know that something is /B, you can't make a conclusion about what happens to C or A because we don't know. you only know that if its NOT B and NOT C then A doesn't happen.
For NC conjunctions, both were not required to meet the condition,
as in M-->O, M-->N, or M--> N and O?
So when the conjunction occurs within the necessary condition, like one or the other can be triggered? So, M--> O or M--> N or does it still need both to happen, but maybe not at the same time
@MarisolSanchez Both will be triggered. M is sufficient to infer both N and O, so if M occurs, both N and O also occur. The conditional phrase mentioned nothing about time.
Resolved!
For the last bit, where the events in the necessary condition branch off, what does that imply about the temporality of the condition? Like, when M is adopted, that guarantees that N and O will be adopted. The branching path seems to say that when M is adopted, either N or O is adopted. Going down one path would seem to preclude the other. Rather the explanation here seems to say that both of those events can happen simultaneously. Is that true?
I can see where that comes from because of how it is displayed. I think try and think about it not as a branching (because you have to follow both arrows actually, you can't just choose one since they are both a result of M) but as a statement like M->O AND M->N meaning if M occurs, both O AND N occur.