@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
weird because I'm awful at the conditional breakdowns when trnslating to lawgic but when we reading the whole paragraph of text I can break it down to where the chain makes sense. Nice!
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
@gabbadoodle /N --> /M OR /O --> /M would be correct. M not being adopted is the necessary condition if either N or O is not adopted, so a negation of one automatically means a negation of M. Although it's true that if both aren't adopted then M can't be adopted, only one needs to be negated to trigger the necessary condition.
Is it intentional that we are not immediately diagramming the counterfactuals for these? Would be helpful to confirm our logic. For example in the last example I initially plotted " M --> N OR O" which I assume is the counterfactual to "/N OR /O --> /M" #feedback thanks
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.'"
Can someone help me with disjunction in the necessary condition? How is it possible that if I say something like
If it's Tuesday, then the store has a sale on liquor or tomatoes
Tu → Li or To
How could OR be used in this way and it's a possibility that on a Tuesday they run a sale on both liquor and tomatoes? Wouldn't OR mean that it needs to be one or the other, but cannot be both?
It could be both, we aren't given enough information to definitively say. All we know is that AT LEAST one, whether liquor or tomatoes, is on sale if it is a Tuesday. AKA - There must be a sale of at least liquor or at least tomatoes if it is indeed a Tuesday. Both could be on sale, or only the liquor or only the tomatoes. But if neither are on sale, then we know it is not a Tuesday. Hope this helps!
#help for the second example "If N or O is not adopted, then M cannot be adopted.," why does "cannot" not trigger the group 4 rule (pick idea and negate necessary condition)?
Hi, I believe "cannot" does not trigger the group 4 rule because when you consider the sentence as a whole, the statement follows the outline of "if A, then B." As a result, you are already following group 1 sufficiency.
Also, you could always try following group 4 and see if it makes sense if you're unsure. If we follow the group 4 rule, it would be the following in lawgic:
/N or /O -> M
In English, it would be something along the lines of:
If N or O is not adopted, then M will be adopted.
Now translated, we can compare our results with the original statement. Through this, it can be seen that group 4's logic does not align with the original statement.
Ultimately, the ability to distinguish which group logic/rule to use will become more intuitive through practice and time. If I missed anything or misunderstood a part, feel free to follow up.
#feedbackHELP!!!! Okay need someone to help for this. Do I have this correct. A--B or C. Do we know that if they tell us that A happened and we know that B didn't happen then what must be true is that C happened right.
Hi, my understanding is that A —> B or C & we are informed that A occurred and B did not occur, this means that C must have occurred because A triggered either B or C reaction. We would use a process of elimination and know C occurred since we know B was not triggered. As a result, I believe you are correct in your understanding.
The only thing to be mindful of is when A —> B or C if we are NOT informed that B did not occur and ARE informed C did occur, this does not automatically B did not occur, it is still possible B occurred.
#Help What if it is said "If N or O is adopted, then M will be adopted."? Would that mean that if N is adopted but O is not, M is adopted? Or do both have to be adopted? I believe it would work if just one is but not sure.
Yes, as if it is in the sufficient, the adoption of N or O are independently sufficient to trigger the adoption of M. O could be thrown off a cliff but if we have N then we will get M as well. Or N could be thrown off a cliff, but if we have O, we are getting M.
I understand that one of two sufficient conditions is enough to fulfill the necessary condition, but I am struggling to understand how two conditional claims in the necessary condition with one sufficient condition create a valid argument? Any insight team?
Hey Kevin I need clarification. In this example I completely understand when using logic. Sufficient disjunction means If A or B-----C. I see what that means if A happens or B happens then it garunetees C. Now with sufficient disjunction I completely understand Or If A--B or C. Meaning that if A happens and B doesn't happen then c Happens right? Im just having a hard time understanding why or in the necessary condition is different than and? in the previous lesson.
Yes absolutely that clarifies it thank you so much. It's hard for me to move past mere rote memorization without complete understanding. Now I see
That IF A---B and C.
You cannot have A without B and C together.
I guess where the confusion is in this tree A where its splits off to the two necessary conditions independent of each other. That means that they are only independent of each other once A comes then they are no longer independent you have to have both.
B and C are independent of each other in that knowing the B is true doesn't tell you anything about C. And knowing that C is true doesn't tell you anything about B. In addition, if B is NOT true, that doesn't tell you anything about C. And if C is NOT true, that doesn't tell you anything about B.
IF A is true, then you know that both B and C are true. So B and C have a conditional relationship to A. But B and C don't have any conditional relationship to each other.
"If there's a blizzard, there will be traffic AND school will be closed."
Let's say tomorrow you know there will be traffic. Does that tell you whether the school is closed tomorrow? NO, because you don't know whether there's a blizzard. IF there's blizzard, then both traffic and school closure. But if all you know is that there will be traffic, you can't conclude anything else.
If A happens, then at least one of B or C must happen.
"If A --> B AND C"
If A happens, then both B and C must happen.
"If X or Y --> Z"
If either X or Y (or both) happen, then Z happens. In other words, X is sufficient for Z. And Y is also sufficient for Z. Another way to put it is, if at least one of X or Y is true, then Z is true.
"If X AND Y --> Z"
The presence of X and Y, together, are sufficient for Z. But if all I know is that X is true, but I don't know anything about Y, then I don't know whether Z is true. Same thing with Y -- if all I know is that Y is true, but I don't know anything about X, I don't know whether Z is true.
Thank you Kevin. Now when there is "and" in the necessary
A-----B and C. Why is B independent of C? That's the part I don't get. Now, I can look at the explanation and see OK that's the way it is and follow that rule. But I don't understand the concept of it fundamentally. What you're saying is if a happens, then
B and C happens so
A----B AND C. But what your also saying when "and" is used as a conjunction in the necessary condition what you are saying is there are two conclusion.
A-----B and C
=1. A----B
2. A----C and either can can happen independently of each other. I just don't get why.
I kinda understand but I might get it confused with the conjunctive 'and' since it seems to me like necessary and sufficient are opposite with and & or?
I’m still a little confused hopefully someone can help me out with the first example. If the Chancellor succeeds that means that Amidala failed or the Jedi’s failed. So we’re saying that it’s necessary for Amidala or the Jedi to fail or both. I think my confusion is not being able to split the arrow, is it that CS-> AF or CS-> JF reads Chancellor succeeds so Amidala failed or Chancellor succeeds so Jedi’s failed.
So are we operating from a place of assumption? Basically assuming that since the Chancellors plan succeeded that either Amidala failed or JF failed.
So either one of two options failed or both and we know that that happened because the chancellor plan succeeded.
If I’m speaking in circles I apologize I am just trying to understand it in as simple terms as possible.
Hey there, I was confused on when to separate with the arrows too. From what I understand, it all comes down to where we have the indicator disjunction. Is it in the sufficient (A) or necessary (B)? If its in the sufficient part (A) that is where we can split AF & JF with two arrows pointing to CS.
Just showing my work:
If the Chancellor succeeds that means that Amidala failed or the Jedi’s failed.
A-Chancellor succeeds (CS); B- Amidala failed or the Jedi’s failed (AF or JF)
Since we only know at least 1 of the pieces of B-the necessary condition has to be true, but we don't know if both could happen, we can't separate AF from JF.
If we have AF or JF in A's place, "Splitting the arrow" means these two sufficient conditions are independent from each other.
I'm having difficulty understanding why disjunction in the necessary condition can't be visually represented by "splitting the arrow."
The first example states, "If the Chancellor's nefarious plan succeeds, then either Amidala failed to convince the Senate or the Jedi Knights failed their mission." According to 7Sage, "at least one (but possibly both) of the two conditions must trigger when the sufficient condition triggers." Couldn't that be drawn like this?
AF
↗
CS
↘
JF
In this diagram (at least, the way I'm interpreting it), the Chancellor's plan succeeding (CS) could trigger Amidala failing to convince the Senate (AF). It could trigger Jedi Knights failing their mission (JF). Alternatively, it could trigger BOTH AF and JF. Doesn't that accord with this statement: "At least one (but possibly both) of the two conditions must trigger when the sufficient condition triggers"?
I have a hypothesis about what my misunderstanding might be. Perhaps the diagram above implies that BOTH AF and JF will trigger if CS is triggered (which doesn't leave room for the "or" interpretation). In other words, the way I've drawn it suggests that AF and JF can't happen independently of each other (BOTH must happen if CS happens, which isn't what the sentence says). Is that where I'm going wrong?
#help
EDIT: Sorry my diagram isn't showing up properly, but you get what I'm trying to say haha.
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.
Yeah, "v = or," and "^ = and," but it probably requires more effort to remember those symbols and distinguish between them. Diagramming is only a tool to help us understand the validity of the argument, so it's unnecessary to add more complexity since the LSAT is already complex enough :)
But if you are already comfortable with them, you can definitely use them.
I personally always confuse the two so I prefer writing the words out.
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69 comments
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.
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
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
weird because I'm awful at the conditional breakdowns when trnslating to lawgic but when we reading the whole paragraph of text I can break it down to where the chain makes sense. Nice!
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)
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
I am confused by the sufficient disjunction. Do you need BOTH /N and /O to have /M? Or is it correct to say that /N --> /M OR /O --> /M?
@gabbadoodle /N --> /M OR /O --> /M would be correct. M not being adopted is the necessary condition if either N or O is not adopted, so a negation of one automatically means a negation of M. Although it's true that if both aren't adopted then M can't be adopted, only one needs to be negated to trigger the necessary condition.
Is it intentional that we are not immediately diagramming the counterfactuals for these? Would be helpful to confirm our logic. For example in the last example I initially plotted " M --> N OR O" which I assume is the counterfactual to "/N OR /O --> /M" #feedback thanks
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.'"
would it also make sense to visualize it like this?
If A, then B or C.
A
--> B
--> C
--> B and C
(imagine the arrows are all coming from the "A" lol)
Yes, I think so, but we have to remember that just because B has happened, that doesn't allow us to conclude C has or hasn't.
#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.
Can someone help me with disjunction in the necessary condition? How is it possible that if I say something like
If it's Tuesday, then the store has a sale on liquor or tomatoes
Tu → Li or To
How could OR be used in this way and it's a possibility that on a Tuesday they run a sale on both liquor and tomatoes? Wouldn't OR mean that it needs to be one or the other, but cannot be both?
It could be both, we aren't given enough information to definitively say. All we know is that AT LEAST one, whether liquor or tomatoes, is on sale if it is a Tuesday. AKA - There must be a sale of at least liquor or at least tomatoes if it is indeed a Tuesday. Both could be on sale, or only the liquor or only the tomatoes. But if neither are on sale, then we know it is not a Tuesday. Hope this helps!
#help for the second example "If N or O is not adopted, then M cannot be adopted.," why does "cannot" not trigger the group 4 rule (pick idea and negate necessary condition)?
thank you for your reply - that totally makes sense. appreciate your help!
Hi, I believe "cannot" does not trigger the group 4 rule because when you consider the sentence as a whole, the statement follows the outline of "if A, then B." As a result, you are already following group 1 sufficiency.
Also, you could always try following group 4 and see if it makes sense if you're unsure. If we follow the group 4 rule, it would be the following in lawgic:
/N or /O -> M
In English, it would be something along the lines of:
If N or O is not adopted, then M will be adopted.
Now translated, we can compare our results with the original statement. Through this, it can be seen that group 4's logic does not align with the original statement.
Ultimately, the ability to distinguish which group logic/rule to use will become more intuitive through practice and time. If I missed anything or misunderstood a part, feel free to follow up.
#feedbackHELP!!!! Okay need someone to help for this. Do I have this correct. A--B or C. Do we know that if they tell us that A happened and we know that B didn't happen then what must be true is that C happened right.
Hi, my understanding is that A —> B or C & we are informed that A occurred and B did not occur, this means that C must have occurred because A triggered either B or C reaction. We would use a process of elimination and know C occurred since we know B was not triggered. As a result, I believe you are correct in your understanding.
The only thing to be mindful of is when A —> B or C if we are NOT informed that B did not occur and ARE informed C did occur, this does not automatically B did not occur, it is still possible B occurred.
#Help What if it is said "If N or O is adopted, then M will be adopted."? Would that mean that if N is adopted but O is not, M is adopted? Or do both have to be adopted? I believe it would work if just one is but not sure.
Yes, as if it is in the sufficient, the adoption of N or O are independently sufficient to trigger the adoption of M. O could be thrown off a cliff but if we have N then we will get M as well. Or N could be thrown off a cliff, but if we have O, we are getting M.
So, in:
If N or O are not adopted then M is not adopted.
Ans:
/N or /O -> /M
/N -> O and /O -> N
so , conclusion scenario 1- N -> /O -> M
conclusion scenario 2- O -> /N -> M
So, am I right if I am analyzing it this way?
I understand that one of two sufficient conditions is enough to fulfill the necessary condition, but I am struggling to understand how two conditional claims in the necessary condition with one sufficient condition create a valid argument? Any insight team?
If it's Monday, I will go to the gym or do laundry.
It's Monday.
So, I will go to the gym or do laundry (I will do at least one of those things).
Is this the kind of argument you're asking about? Sorry, not sure what you're referring to.
Hey Kevin I need clarification. In this example I completely understand when using logic. Sufficient disjunction means If A or B-----C. I see what that means if A happens or B happens then it garunetees C. Now with sufficient disjunction I completely understand Or If A--B or C. Meaning that if A happens and B doesn't happen then c Happens right? Im just having a hard time understanding why or in the necessary condition is different than and? in the previous lesson.
Yes absolutely that clarifies it thank you so much. It's hard for me to move past mere rote memorization without complete understanding. Now I see
That IF A---B and C.
You cannot have A without B and C together.
I guess where the confusion is in this tree A where its splits off to the two necessary conditions independent of each other. That means that they are only independent of each other once A comes then they are no longer independent you have to have both.
"A --> B and C"
B and C are independent of each other in that knowing the B is true doesn't tell you anything about C. And knowing that C is true doesn't tell you anything about B. In addition, if B is NOT true, that doesn't tell you anything about C. And if C is NOT true, that doesn't tell you anything about B.
IF A is true, then you know that both B and C are true. So B and C have a conditional relationship to A. But B and C don't have any conditional relationship to each other.
"If there's a blizzard, there will be traffic AND school will be closed."
Let's say tomorrow you know there will be traffic. Does that tell you whether the school is closed tomorrow? NO, because you don't know whether there's a blizzard. IF there's blizzard, then both traffic and school closure. But if all you know is that there will be traffic, you can't conclude anything else.
Does this make sense?
"If A --> B or C."
If A happens, then at least one of B or C must happen.
"If A --> B AND C"
If A happens, then both B and C must happen.
"If X or Y --> Z"
If either X or Y (or both) happen, then Z happens. In other words, X is sufficient for Z. And Y is also sufficient for Z. Another way to put it is, if at least one of X or Y is true, then Z is true.
"If X AND Y --> Z"
The presence of X and Y, together, are sufficient for Z. But if all I know is that X is true, but I don't know anything about Y, then I don't know whether Z is true. Same thing with Y -- if all I know is that Y is true, but I don't know anything about X, I don't know whether Z is true.
Thank you Kevin. Now when there is "and" in the necessary
A-----B and C. Why is B independent of C? That's the part I don't get. Now, I can look at the explanation and see OK that's the way it is and follow that rule. But I don't understand the concept of it fundamentally. What you're saying is if a happens, then
B and C happens so
A----B AND C. But what your also saying when "and" is used as a conjunction in the necessary condition what you are saying is there are two conclusion.
A-----B and C
=1. A----B
2. A----C and either can can happen independently of each other. I just don't get why.
I kinda understand but I might get it confused with the conjunctive 'and' since it seems to me like necessary and sufficient are opposite with and & or?
I’m still a little confused hopefully someone can help me out with the first example. If the Chancellor succeeds that means that Amidala failed or the Jedi’s failed. So we’re saying that it’s necessary for Amidala or the Jedi to fail or both. I think my confusion is not being able to split the arrow, is it that CS-> AF or CS-> JF reads Chancellor succeeds so Amidala failed or Chancellor succeeds so Jedi’s failed.
So are we operating from a place of assumption? Basically assuming that since the Chancellors plan succeeded that either Amidala failed or JF failed.
So either one of two options failed or both and we know that that happened because the chancellor plan succeeded.
If I’m speaking in circles I apologize I am just trying to understand it in as simple terms as possible.
Hey there, I was confused on when to separate with the arrows too. From what I understand, it all comes down to where we have the indicator disjunction. Is it in the sufficient (A) or necessary (B)? If its in the sufficient part (A) that is where we can split AF & JF with two arrows pointing to CS.
Just showing my work:
If the Chancellor succeeds that means that Amidala failed or the Jedi’s failed.
A-Chancellor succeeds (CS); B- Amidala failed or the Jedi’s failed (AF or JF)
Since we only know at least 1 of the pieces of B-the necessary condition has to be true, but we don't know if both could happen, we can't separate AF from JF.
If we have AF or JF in A's place, "Splitting the arrow" means these two sufficient conditions are independent from each other.
Is saying "inclusive or" the same thing as saying "and or"?
I'm having difficulty understanding why disjunction in the necessary condition can't be visually represented by "splitting the arrow."
The first example states, "If the Chancellor's nefarious plan succeeds, then either Amidala failed to convince the Senate or the Jedi Knights failed their mission." According to 7Sage, "at least one (but possibly both) of the two conditions must trigger when the sufficient condition triggers." Couldn't that be drawn like this?
AF
↗
CS
↘
JF
In this diagram (at least, the way I'm interpreting it), the Chancellor's plan succeeding (CS) could trigger Amidala failing to convince the Senate (AF). It could trigger Jedi Knights failing their mission (JF). Alternatively, it could trigger BOTH AF and JF. Doesn't that accord with this statement: "At least one (but possibly both) of the two conditions must trigger when the sufficient condition triggers"?
I have a hypothesis about what my misunderstanding might be. Perhaps the diagram above implies that BOTH AF and JF will trigger if CS is triggered (which doesn't leave room for the "or" interpretation). In other words, the way I've drawn it suggests that AF and JF can't happen independently of each other (BOTH must happen if CS happens, which isn't what the sentence says). Is that where I'm going wrong?
#help
EDIT: Sorry my diagram isn't showing up properly, but you get what I'm trying to say haha.
I think the diagram you drew, like you said, lacks the required "or" factor. It looks like 2 guaranteed outcomes from the premise.
When are the suffients of a disjunction not independent of each other?
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
Does anyone know why we are not using logic symbols? Ex: ~ is the logic symbol for not and v is the logic symbol for or.
Yeah, "v = or," and "^ = and," but it probably requires more effort to remember those symbols and distinguish between them. Diagramming is only a tool to help us understand the validity of the argument, so it's unnecessary to add more complexity since the LSAT is already complex enough :)
But if you are already comfortable with them, you can definitely use them.
I personally always confuse the two so I prefer writing the words out.