is the itermediary in the transformation from an embeded conditional into a joint sufficient conditional a conditional conclusion in the previous lesson?
Maybe this will help to understand it more. Let's work with this rule:
If you are a member, then either you pay dues or you are expelled
So, first we put the logic chain as it is and remember, in the "or" one has to be negative (it's easier for me to always put the sufficient negative): M → (/P → E)
Then, we grab the sufficient clause of the second relationship and put it in the sufficient side of the whole chain (if it is negative, it passes as negative not as positive): M and /P → E
I think I understand but this is wholly reliant upon the other way being true as well:
So I understand that if I live in a building with 10+ units and I’ve kept my pet openly and notoriously then I have the right to keep a pet. By saying the contrapositive of the other necessary option ( R and /opno) I’m ruling out that option and since it has to be one option, then that would have to mean I have the right.
BUT please confirm then that if I live in a building with 10+ units and I don’t have the right to keep my pet then that means my pet has not been chilling with me openly and notoriously.
I just want to make sure that would follow logically, in reality it makes perfect sense and I see people in my apartment complex sneak with their dogs all the time bc we live in a building with 10+ units and we don’t have the right to have pets lol.
@BumbleBee22 I tried the same thing and I used this prompt and it helped me "can you better explain the following concept in a easier way for me to understand:
This took my a while but I think I understand it in my own way: disjunctions show two alternatives if A then B happens or C happens. BUT an embedded conditional is when "if A then B happens and if B happens then that triggers something to happen in C".
@IsabelSafar Disjunctions show alternative possibilities, while an embedded conditional shows a causal relationship.
"If M gets adopted, either O gets adopted or P gets adopted"
Disjunction: M-> (O or P)
There are 2 possible outcomes if M gets adopted - Either O gets adopted or P gets adopted.
An Embedded Conditional would be: M -> (/O -> P)
If M gets adopted, and O does not get adopted, then P gets adopted. This could also be structured the other way [M->(/P->O)] which would indicate if M gets adopted, and P does not get adopted, then O gets adopted.
The embedded conditional breaks down what the outcome of what one of the "or" could be. Some questions on the LSAT may be structured this way rather than as an "or" and this is a method to unpack/unembed it to better understand.
The Unembedded Conditional would be:
M and /O -> P (if M gets adopted and O does not get adopted then P gets adopted)
this may be a stupid question, but how do you even know if you have an embedded conditional from the English text alone. I can obviously identify it in its logic form given the parentheses, but I am having trouble with identifying it when it is in English...
could someone help? do you have any other examples of English text that contains embedded conditionals?
@IsabelSafar I used AI to check this before posting, but from my understanding, it’s: if A happens, then either B must occur or C (or both) must occur in order for A to be true.
“if,” “whenever,” “when” → introduces A (trigger)
“either…or…” → signals B ∨ C
“only if,” “requires,” “unless” → introduces necessary condition (B or C)
Can embedded conditionals also apply to conjunctions in the NC? ex: if B then (A and C) becomes if B and A then C? and if a conditional for examples is /A-->(B-->C) becomes /A and B, then C? @Kevin_Lin
Based on that, it is true to say that "(B and A) --> C". But this isn't really a restatement of the relationship. The reason that statement would be true is because we know that B guarantees C. So it's also true that we know B and A are true, C must be true, too (because of B). But this statement leaves out the idea that B also guarantees A. So if you just say "If B and A are true, then C must be true," this doesn't capture the original idea that B guarantees both A and C.
/A --> (B --> C).
You can rephrase this as you describe -- (/A and B) --> C.
I have a suggestion after reviewing the lesson multiple times over more than a 6 month period. I was confused with this technique because for me initially I looked at the first step as creating the conjunct. I broke it down like this, and using CC on the video helped me as well, to understand. (1) Write the Rule, (2) Apply the translation rule, (3) Take the inside sufficient condition from the embedded condition and create a conjunction with the outside necessary condition. I, also would like to make the recommendation on the review slide to label ( Embedded Sufficient Condition, Embedded Necessary Condition, and Outside Necessary Condition). When looking at the review slide I did not at first know what to distinguish, until I caught myself reviewing the lessons multiple times and using CC, to see what I was missing. For, me as I have used 7 sage just watching the video without CC has caused me to miss things. I hope this is helpful.
I don't get why you can replace the 'or' for an arrow. Which lesson was this? I remember the negation and then flipping the two sides of the arrow, but not switching in between arrows and 'or' statements
@laurenstudies came here to make this exact comment lol.
I guess the idea is that the “or” becomes an arrow if we’re also negating one of the disjuncts.
If you live in NYC then you either Filed Taxes, or Paid Penalty aka NYC > (FT or PP)
so if you did not File Taxes aka /FT, you must have Paid the Penalty.
NYC > /FT > PP
that’s also where the whole combining the sufficient of the embedded conditional comes in. /FT > PP is an embedded conditional (If no Filed Taxes, then Paid Penalty). So we can simplify this by saying
@monmon Nice! One minor thing I'll note is that when you represent NYC > /FT > PP, remember to keep parens around (/FT > PP); otherwise that would imply that NYC > /FT, which isn't quite what you mean.
okay i understand when the sentance uses the indicator "or" but what if the embedded sentences dont use "or" how are we supposed to simplify the embedded conditional. and the example he gives, to me is more of a normal conditional with a disjunction in the necessary position. why do we consider this an embedded conditional?
If a resident lived in a building with more than ten units, then either she has an inalienable right to keep a pet or she has not kept that pet openly and notoriously.
B10+ → (R or /OpNo)
Apply rule 3 (negate sufficient)
B10+ → (R or /OpNo) to B10+ → (OpNo → R)
He chose to negate OpNo to not deal with a negative, but you can negate R first .
If a resident lived in a building with more than ten units, she has kept that pet openly and notoriously, has an inalienable right to keep a pet.
The or is still a conditional indicator with a sufficient and necessary. Since we did rule 3 above the sufficient is now OpNo and necessary is R
Remember there is an inclusive either/or sometimes meaning 'and'. That is what he is doing here. He dropped the parenthesis to conjoin the two sufficiecy B10+ and OpNo
The first one needs to add parentheses around the final conditional:
Jack walks -> (/store -> movies)
That means if jack walks, then if he doesn't go to the store, he must go to the movies.
The second one isn't true, because it implies that he can only go to one out of the store or movies. But saying "he will go to the store or the movies" still allows him to go to both. It just means he'll go to at least one of them.
just to clarify, does A and B --> C mean the same as (A and B) --> C? Like the statement is NOT A, also B --> C? The parenthesis existing sometimes but not always is a bit hard to wrap one's head around, especially with any background in math. thank you!
@SusanLeifker Right -- if we have both A and B, then we know that C must be true. The parens helps us avoid that second interpretation ("A is true. Also, If B, then C.")
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180 comments
chile....
is the itermediary in the transformation from an embeded conditional into a joint sufficient conditional a conditional conclusion in the previous lesson?
What is the difference between the Disjunction and Embedded Conditionals?
Disj: a --> B or C (or both) [but embedded is not like that - - what is the difference and how do you know (how to tell the difference in ORs apart?)]
Embedded: if A --> then B and Not C (and vis versa)
Also does the word either trigger the one or the other condition of or?
Is disjunctive or equal inclusive or and embedded or equal exclusive or?
Maybe this will help to understand it more. Let's work with this rule:
If you are a member, then either you pay dues or you are expelled
So, first we put the logic chain as it is and remember, in the "or" one has to be negative (it's easier for me to always put the sufficient negative): M → (/P → E)
Then, we grab the sufficient clause of the second relationship and put it in the sufficient side of the whole chain (if it is negative, it passes as negative not as positive): M and /P → E
I think I understand but this is wholly reliant upon the other way being true as well:
So I understand that if I live in a building with 10+ units and I’ve kept my pet openly and notoriously then I have the right to keep a pet. By saying the contrapositive of the other necessary option ( R and /opno) I’m ruling out that option and since it has to be one option, then that would have to mean I have the right.
BUT please confirm then that if I live in a building with 10+ units and I don’t have the right to keep my pet then that means my pet has not been chilling with me openly and notoriously.
I just want to make sure that would follow logically, in reality it makes perfect sense and I see people in my apartment complex sneak with their dogs all the time bc we live in a building with 10+ units and we don’t have the right to have pets lol.
WHAT IS ACTUALLY HAPPENING OMG --- THEY LOST ME AFTER "KICKING UP CONDITIONAL" IM ACTUALLY SOOO LOST ---MY MONEY GOING TO NOTHING AAAAAAAAAAAAA
@ratman23 Never mind -- chatGPT just saved me lol ---sorry for the crash out heheheheh
@ratman23 omg what was your prompt because I HAVE NO IDEA WHAT IS GOING ON
@BumbleBee22 I tried the same thing and I used this prompt and it helped me "can you better explain the following concept in a easier way for me to understand:
@BumbleBee22 I copied and pasted all the notes from the bottom, put it into ChatGPT, and said, I don't understand, please simplify and explain.
Can someone clarify the difference between embedded conditionals v. conjunction.
lol wth is this!!
@Reddrum0911 SAMEEEE BRUUU
@Reddrum0911 lmaooooo
This took my a while but I think I understand it in my own way: disjunctions show two alternatives if A then B happens or C happens. BUT an embedded conditional is when "if A then B happens and if B happens then that triggers something to happen in C".
@mahi0615 u MAKE MORE SENSE THAN THE VIDEO
@ratman23 I'm flattered haha
what's the difference between an embedded conditional and a disjunction?? this feels the same to me as the example:
If M gets adopted, either O gets adopted or P gets adopted
M --> O or P
@IsabelSafar Disjunctions show alternative possibilities, while an embedded conditional shows a causal relationship.
"If M gets adopted, either O gets adopted or P gets adopted"
Disjunction: M-> (O or P)
There are 2 possible outcomes if M gets adopted - Either O gets adopted or P gets adopted.
An Embedded Conditional would be: M -> (/O -> P)
If M gets adopted, and O does not get adopted, then P gets adopted. This could also be structured the other way [M->(/P->O)] which would indicate if M gets adopted, and P does not get adopted, then O gets adopted.
The embedded conditional breaks down what the outcome of what one of the "or" could be. Some questions on the LSAT may be structured this way rather than as an "or" and this is a method to unpack/unembed it to better understand.
The Unembedded Conditional would be:
M and /O -> P (if M gets adopted and O does not get adopted then P gets adopted)
this may be a stupid question, but how do you even know if you have an embedded conditional from the English text alone. I can obviously identify it in its logic form given the parentheses, but I am having trouble with identifying it when it is in English...
could someone help? do you have any other examples of English text that contains embedded conditionals?
@IsabelSafar I used AI to check this before posting, but from my understanding, it’s: if A happens, then either B must occur or C (or both) must occur in order for A to be true.
“if,” “whenever,” “when” → introduces A (trigger)
“either…or…” → signals B ∨ C
“only if,” “requires,” “unless” → introduces necessary condition (B or C)
This was how I understood it:
If a resident lives in a building with more than ten units...
If is a sufficient indicator so this statement is on the left B10+
then either she has an inalienable right to keep a pet or she has not kept that pet openly and notoriously.
Then is a necessary indicator so everything is on the right of the arrow because we must have this
R or /OpNo
We put it together
B10+ --> (R or /OpNo)
It still doesn't make sense so we follow the sufficient negate rule of (or)
So now my rule says
B10+ --> (OpNo or R)
Well I can make it even more clear and pull out the inside sufficient condition to make it a sufficient conjunct in the outside conditional
My Final rule says
B10+ and OpNo -->R
sometimes you just have to come back to something 2 months later to understand it
Can embedded conditionals also apply to conjunctions in the NC? ex: if B then (A and C) becomes if B and A then C? and if a conditional for examples is /A-->(B-->C) becomes /A and B, then C? @Kevin_Lin
Thanks
@hvw
If B, then both A and C.
Based on that, it is true to say that "(B and A) --> C". But this isn't really a restatement of the relationship. The reason that statement would be true is because we know that B guarantees C. So it's also true that we know B and A are true, C must be true, too (because of B). But this statement leaves out the idea that B also guarantees A. So if you just say "If B and A are true, then C must be true," this doesn't capture the original idea that B guarantees both A and C.
/A --> (B --> C).
You can rephrase this as you describe -- (/A and B) --> C.
@Kevin_Lin Thank you
I have a suggestion after reviewing the lesson multiple times over more than a 6 month period. I was confused with this technique because for me initially I looked at the first step as creating the conjunct. I broke it down like this, and using CC on the video helped me as well, to understand. (1) Write the Rule, (2) Apply the translation rule, (3) Take the inside sufficient condition from the embedded condition and create a conjunction with the outside necessary condition. I, also would like to make the recommendation on the review slide to label ( Embedded Sufficient Condition, Embedded Necessary Condition, and Outside Necessary Condition). When looking at the review slide I did not at first know what to distinguish, until I caught myself reviewing the lessons multiple times and using CC, to see what I was missing. For, me as I have used 7 sage just watching the video without CC has caused me to miss things. I hope this is helpful.
I don't get why you can replace the 'or' for an arrow. Which lesson was this? I remember the negation and then flipping the two sides of the arrow, but not switching in between arrows and 'or' statements
@laurenstudies came here to make this exact comment lol.
I guess the idea is that the “or” becomes an arrow if we’re also negating one of the disjuncts.
If you live in NYC then you either Filed Taxes, or Paid Penalty aka NYC > (FT or PP)
so if you did not File Taxes aka /FT, you must have Paid the Penalty.
NYC > /FT > PP
that’s also where the whole combining the sufficient of the embedded conditional comes in. /FT > PP is an embedded conditional (If no Filed Taxes, then Paid Penalty). So we can simplify this by saying
NYC and /FT > PP
@monmon thanks for providing ur thought process for this!! yeah the and's and or's and conditionals inside conditionals can feel so complicated haha
@laurenstudies "or" is in Group 3 that's why. See the group 3 lesson in "Conditional and Set Logic"
@monmon Nice! One minor thing I'll note is that when you represent NYC > /FT > PP, remember to keep parens around (/FT > PP); otherwise that would imply that NYC > /FT, which isn't quite what you mean.
@Kevin_Lin thank you for that! I appreciate the insight—the parentheses do change the meaning
If I go to the Gym on Sunday, then I will do cardio OR lift weights.
Gym on Sunday --> Cardio OR lift weights
Gym on Sunday --> (/Cardio OR lift weights)
Gym on sunday and /Cardio --> Lift weights
how do we know when to use it?
@marlenevelazquez #help
this audio is hard to listen to <3
If the toddler throws a tantrum then they're tired or mad.
tantrum --> tired or mad
tantrum --> (/mad --> tired)
tantrum and /mad --> tired
okay i understand when the sentance uses the indicator "or" but what if the embedded sentences dont use "or" how are we supposed to simplify the embedded conditional. and the example he gives, to me is more of a normal conditional with a disjunction in the necessary position. why do we consider this an embedded conditional?
can someone please explain how it went from B10+ -> (R or /OpNo) to B10+ (OpNo -> R)? Did I forget a rule? That part is tripping me up.
@gabbergabs
The original statement is:
If a resident lived in a building with more than ten units, then either she has an inalienable right to keep a pet or she has not kept that pet openly and notoriously.
B10+ → (R or /OpNo)
Apply rule 3 (negate sufficient)
B10+ → (R or /OpNo) to B10+ → (OpNo → R)
He chose to negate OpNo to not deal with a negative, but you can negate R first .
If a resident lived in a building with more than ten units, she has kept that pet openly and notoriously, has an inalienable right to keep a pet.
The or is still a conditional indicator with a sufficient and necessary. Since we did rule 3 above the sufficient is now OpNo and necessary is R
Remember there is an inclusive either/or sometimes meaning 'and'. That is what he is doing here. He dropped the parenthesis to conjoin the two sufficiecy B10+ and OpNo
B10+ and OpNo → R
@amhuynh thank you!
If Jack walks he will go to the store or the movies.
Jack walks → store or movie
It becomes
Jack walks → /store → movies
Jack walks → store →/movies
@NhubriaChikaka Almost!
The first one needs to add parentheses around the final conditional:
Jack walks -> (/store -> movies)
That means if jack walks, then if he doesn't go to the store, he must go to the movies.
The second one isn't true, because it implies that he can only go to one out of the store or movies. But saying "he will go to the store or the movies" still allows him to go to both. It just means he'll go to at least one of them.
just to clarify, does A and B --> C mean the same as (A and B) --> C? Like the statement is NOT A, also B --> C? The parenthesis existing sometimes but not always is a bit hard to wrap one's head around, especially with any background in math. thank you!
@SusanLeifker my brain wants to PEMDAS lawgic LOL
@SusanLeifker Right -- if we have both A and B, then we know that C must be true. The parens helps us avoid that second interpretation ("A is true. Also, If B, then C.")
if you are reading this, you got this!! I believe in you!
@SusanLeifker You too girl!!!
@NhubriaChikaka ty!!!