@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 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.
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.
Statement A: If Bill (B) and Mary (M) are adopted, then I (A) am adopted.
If B and M, then A
= B and M->A
= (B∩M)->A
= /A->/B ∪ /M
=/A->/B or /M or both not (inclusive or)
If I am not adopted, then either Bill or Mary is not adopted, or both are not adopted.
Statement B: If I (A) am adopted, then both Bill (B) and Mary (M) are adopted.
If I, then B and M
= A-> B and M
=A->(B∩M)
= /B ∪ /M or both not (inclusive or)-> /A
If either Bill or Mary is not adopted, or both are not adopted, then I am not adopted
You can use the same method to negate for sentences using "or" as the conjunction. As set theory OR (A or B, or both AB) is an inclusive or like the LSAT. Exclusive or is either A or B, no union represented by XOR.
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.
@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.
#feedback HELP!!. Why when and is used as a conduction in a sufficient condition does it mean you must have both of these things to have the necessary condition. Why is it not the same when and as a conjunction is used in the necessary condition? Is it not saying If A---B and C
So what you're saying is if you have A then you can have b or c. Im just having a hard time in understanding why that is the case.
Same -- but after looking through the lesson and comments it seems as though each part of the “and” is required separately when the sufficient condition happens. So basically if the necessary has the "and," then they both do have to happen but it is normally shown with separate statements rather than together like you would see if the conjunction was in the sufficient condition.
- 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.
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.
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.
why does the sentence "If Amidala convinces the Senate and the Jedi Knights accomplish their mission, then the Chancellor's nefarious plan will fail." translate into A and J → CF?
Hi, what you've said sounds correct to me. I just wanted to point out that I think the contrapositive would be /CF-> /J or /S, and not /J and /S -> /CF.
This is covered in JY's videos/text on de Morgan's law or someplace else I believe. It's because if the Chancellor's plan did not fail (ie failing the necessary condition) then you know for a fact that at least 1 of the two components in the sufficient (J or S) must've failed (as the sufficient was triggered to fail). I think it could also be that both failed, but at least 1 did.
The rest you said sounds good, I just thought I saw a misconception and would've appreciated it if someone corrected me if they thought I made a mistake. Feel free to ask someone else if what I said is correct or not. Hope that helps!
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.
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.
I am a bit confused regarding statement #2. Based on the fact that if the sufficient condition is met then then necessary must be met but in the reverse just because the necessary is met does not imply the sufficient. For the example of if M is adopted then N are 0 are adopted if M -> N+O, based on this statement the contrastive would be if /N+/O -> /M which means that if the necessary is not met then the sufficient is neither can someone please explain why as the arrow cannot move from right to left only left to right? #feedback
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:
No, that wouldn't be a translation. Under "A -> B and C" B and C have no direct relationship to each other. If C is not true, that doesn't imply anything about B.
But under "A and B -> C", if C is not true, that means A is not true or B is not true. So there is a relationship between C and B.
In addition, under the original statement, it's impossible for A to be true while C is not true. But, under "A and B -> C" it's possible that A is true while C is not true (as long as B is not true.)
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70 comments
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.
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.
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.
how to make the contrapositive with "and " in the diagram?
@lilywong
Using set math:
Statement A: If Bill (B) and Mary (M) are adopted, then I (A) am adopted.
If B and M, then A
= B and M->A
= (B∩M)->A
= /A->/B ∪ /M
=/A->/B or /M or both not (inclusive or)
If I am not adopted, then either Bill or Mary is not adopted, or both are not adopted.
Statement B: If I (A) am adopted, then both Bill (B) and Mary (M) are adopted.
If I, then B and M
= A-> B and M
=A->(B∩M)
= /B ∪ /M or both not (inclusive or)-> /A
If either Bill or Mary is not adopted, or both are not adopted, then I am not adopted
You can use the same method to negate for sentences using "or" as the conjunction. As set theory OR (A or B, or both AB) is an inclusive or like the LSAT. Exclusive or is either A or B, no union represented by XOR.
conjunction junction, what's your function?
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?
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'm getting logic games flashbacks lolol
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.
do we need to put brackets around A&J in order to show that both of these need to be satisfied? and not just one?
Resolved!
#feedback HELP!!. Why when and is used as a conduction in a sufficient condition does it mean you must have both of these things to have the necessary condition. Why is it not the same when and as a conjunction is used in the necessary condition? Is it not saying If A---B and C
So what you're saying is if you have A then you can have b or c. Im just having a hard time in understanding why that is the case.
Same -- but after looking through the lesson and comments it seems as though each part of the “and” is required separately when the sufficient condition happens. So basically if the necessary has the "and," then they both do have to happen but it is normally shown with separate statements rather than together like you would see if the conjunction was in the sufficient condition.
- 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 think venn diagrams might be helpful to illustrate how this concept is applied.
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.
It's starting to click!
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.
why does the sentence "If Amidala convinces the Senate and the Jedi Knights accomplish their mission, then the Chancellor's nefarious plan will fail." translate into A and J → CF?
Hi, what you've said sounds correct to me. I just wanted to point out that I think the contrapositive would be /CF-> /J or /S, and not /J and /S -> /CF.
This is covered in JY's videos/text on de Morgan's law or someplace else I believe. It's because if the Chancellor's plan did not fail (ie failing the necessary condition) then you know for a fact that at least 1 of the two components in the sufficient (J or S) must've failed (as the sufficient was triggered to fail). I think it could also be that both failed, but at least 1 did.
The rest you said sounds good, I just thought I saw a misconception and would've appreciated it if someone corrected me if they thought I made a mistake. Feel free to ask someone else if what I said is correct or not. Hope that helps!
wasnt sure about that either. I would assume it would be J and S -> CF
and then /J and /S -> /CF
and that
/J -> ? doesnt conclude anything - plan could fail or not fail
/S -> ? doesnt conclude anyting - plan could fail or not fail
as they dont have a relationship with each other so we would not be able to know what happens if only one of them was /
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.
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 am a bit confused regarding statement #2. Based on the fact that if the sufficient condition is met then then necessary must be met but in the reverse just because the necessary is met does not imply the sufficient. For the example of if M is adopted then N are 0 are adopted if M -> N+O, based on this statement the contrastive would be if /N+/O -> /M which means that if the necessary is not met then the sufficient is neither can someone please explain why as the arrow cannot move from right to left only left to right? #feedback
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 )
if A, then B and C, can that be rewritten to if A and B, then C?
No, that wouldn't be a translation. Under "A -> B and C" B and C have no direct relationship to each other. If C is not true, that doesn't imply anything about B.
But under "A and B -> C", if C is not true, that means A is not true or B is not true. So there is a relationship between C and B.
In addition, under the original statement, it's impossible for A to be true while C is not true. But, under "A and B -> C" it's possible that A is true while C is not true (as long as B is not true.)
Hello, Kevin. Could you confirm whether the following is accurate?
Original:
A and B → C
Valid conditions:
/C → /A or /B
/C → A or /B
/C → /A or B
Thank you!
So in this example "If M is adopted, then N and O are adopted." If M is adopted is that the sufficient condition???
Yes because I thought of it as if there was a priority chart lol. So if M is not adopted then N and O cannot be adopted.
1.M adopted
2.N and O gets adopted
yes