@Oblivion I think it's to signal that the phrases are interchangeable. If Luke is a Jedi <-> then Yoda trained him. If Yoda trained Luke <-> then Luke is a Jedi.
#help Would it make sense if I say like sufficient is like enough for Luke to become a Jedi but there are other ways & for necessary it’s the only way required .
I really wish the time given in the study plan would at least correspond with the length of the video. The study plan claims this is a 2-minute section and the video is 6:49 long. Am I just supposed to ignore the video? This is happening frequently as I go through this study plan.
@thr107 Thanks for bringing this up -- we'll look into this. I think the plan is supposed to reflect the video time when there's a video, so if it's not, something's wonky.
Here, we tackle a special category of conditional relationships: those in which two conditions are both sufficient and necessary for each other. What are Bi-Conditional Claims: They are just the conjunction of a uni-conditional claim and its converse.
Bi-Conditional Claims:
Luke will become a Jedi if Yoda trains him and Luke will become a Jedi only if Yoda trains him
Yoda’s training is sufficient and necessary for Luke becoming a Jedi.
Translating into Lawgic: (yoda - t → luke- j) (luke-j → yoda - t) [&]
Bi-Conditional in Lawgic: (yoda-t) ← (luke-j) it then looks like this (yoda-t ←→ luke-j)
So what does the bi-conditional mean? It means that Yoda’s training is sufficient and necessary for Luke becoming a Jedi.
The contrapositive of this will look like this: (/yoda-t ← → /luke - j)
Indicators for Bi-Condirionals:
If and only if
If but only of
Then and only then
Or…but not both
If…then…but not otherwise
Examples for Bi-Conditionals:
Luke will become a Jedi if and only if Yoda trains him
Luke will become a Jedi if but only if Yoda trains him
Luke will become a Jedi if Yoda trains him but not otherwise.
[These are all sufficient and necessary conditionals]
RECAP:
Uni-conditionals express sufficiency (Yoda’s training is sufficient for Luke to become a Jedi) or necessity (Yoda’s training is necessary for Luke to become a Jedi).
A bi-conditional indicates that the two conditions are both sufficient and necessary for each other (Yoda’s training is both sufficient and necessary for Luke to become a Jedi). They are mutually dependent. One occurs if and only if the other occurs.
Bi-conditionals claims are represented in Lawgic with the bi-conditional arrow: ← →
@dylancameron814 didn’t even look at the lesson and it clicked because of your comment.
Wish they would have used this example:
Student are cited as late only if they arrive more than 5 minutes past home room bell.
Cited late-> 5+
John arrived 17 minutes past the home room bell. Can we logically assume John was cited as late? No. John got a note from his mommy.
Students are cited as late if and only if they arrive more than 5 minutes past homeroom bell.
Cited as late <—> 5+
John arrived more than 17 minutes late. Can we logically assume John received a citation? YES Your Tort professor will not accept notes from your mommy, or doctor or the psychiatrist you visited after finishing this lesson.
Hey, I'm a bit confused about the classification here and would love some clarification!
I understand that a biconditional statement means 'If A then B, and if B then A'—so we can write it like:
A → B = ~A or B
B → A = ~B or A
A ↔ B = (~A or B) and (~B or A)
But I’m having trouble with how 7Sage classifies 'A or B, but not both' as a biconditional indicator. To me, it looks like 'A or B, but not both' is actually more like an exclusive-or (XOR), where it's one or the other, but not both.
For example, 'A or B, but not both' translates to:
(A or B) and ~(A and B) = (A or B) and (~A or ~B)
And that doesn't seem to match up with the biconditional logic, which is why I’m a little confused.
Am I missing something here? Or is there a specific context I’m not considering in how 7Sage is approaching this? I’d really appreciate any insight on this!
@LsatFootpad You're taking the logic of the uniconditional (testing the logic of its contrapositive) and applying it to the biconditional, which won't work. A biconditional is A and B, but not one or the other. Each clause of the biconditional is now sufficient and necessary for the other. They require each other to exist.
Example:
If raining, then cloudy.
If cloudy, then raining.
If it is raining, then it must be cloudy, and if it is cloudy then it must be raining.
It is raining if and only if it is cloudy.
It is cloudy if and only if it is raining.
R <-> C
Whereas if they are uniconditional, then it could be raining and not be cloudy (as seen in Hawaii often,) or it could be cloudy but not raining (as often the case in Seattle, though rain is common there as well.)
If biconditional, let's assume there is a fictional nation, Republic of Precipitation and Overcast Weather. Aptly named.
In this place, the biconditional exists where if it is cloudy then it is 100% raining outside no exception and vice versa, you won't get rain without clouds.
@dvo1d Thanks so much for the explanation! I think I’m starting to get it, but I’m still a bit unsure about how it relates to the original question.
The example you gave about 'If it’s raining, then it must be cloudy, and if it’s cloudy, then it must be raining' makes perfect sense to me as a biconditional: 'If and only if' one condition holds, the other one must hold as well.
However, when I look at the 'Or ... but not both' phrasing, it still seems more like an exclusive-or situation (XOR) to me. In other words, it’s either A or B, but not both at the same time—which feels more like the opposite of a biconditional.
For example, 'Cloudy or Raining, but not both' would work out to:
(Cloudy or Raining) and ~(Cloudy and Raining)
Which, when I compare it to the biconditional you used earlier, seems like a different structure entirely. That’s why I’m wondering if there’s something I’m missing about 7Sage’s interpretation of 'Or ... but not both' as a biconditional indicator. Could someone help me clarify this?
Thanks again for the help! I really appreciate it.
@Sameer_Ahamad the if...then...but not otherwise is an indicator for bi-conditionals meaning it can go either way, the specific lawgic translations you posted could go either way just ensure that both are positive or both are negative.
This clicked (sort of) for me by thinking of it as an exclusion of all other possible causes. In the case of the example sentence, the ONLY path that Luke has to become a Jedi is via being trained by Yoda, and being trained by Yoda is CERTAIN to make him a Jedi.
Therefore, you can derive information in both directions. If Yoda DOES train him then he will become a Jedi. If he DOES become a Jedi Yoda must have trained him.
This is different from typical logical relations where you are limited in what you can know. For example:
if A -> B, the contrapositive is /B -> /A
If we are given information about /A, we do not know what happens in this case because there is no arrow flowing from it to another thing (to egregiously oversimplify the actual mechanism). But if instead we had:
A <-> B and its contrapositive /A <-> /B
We now know what /A causes, it must mean cause /B, whereas in the first case you would not be able to generate any reliable conclusions.
If two events are inextricably linked, and are the sole causes of one another, the "if and only if" wording applies, and you have this certainty that if one event happens, the other MUST as well (no matter which you start from). This logic also applies after negation.
In my opinion the best way to explain/understand a bi-conditional claim is how it is taught in Math. It is taught as an 'iff' claim aka. an if and only if claim.
All an iff claim means is that each element implies the other:
Iff A then B, means: A --> B, and B --> A.
It is helpful to differentiate an iff claim from a regular conditional because of LSAT questions as so:
an animal is a zebra if and only if it has white and black stripes. (our biconditional claim in an argument on the LSAT)
Jerry is an animal that has black and white stripes. (an assertion made as part of the argument)
What inference can you make? (LR question on LSAT)
That Jerry is a zebra. (Answer derived by understanding that it is an iff claim, so both elements imply each other)
@naomiy2k I feel the same way, but honestly, as you move forward I feel like the information starts to subconsciously make sense and you start to apply what you've learnt without necessarily digging deep into the trenches of you brain lol
@naomiy2k To my understanding the kick it up method is not something you need to use when evaluating a conditional claim, but is an option that makes it easier. At the moment I generally have not been thinking about it in drills but I think I eventually will when I train harder levels.
Is it the case for anyone else that you understand how to work out these scenarios in English, but the Lawgic translation then makes it confusing to understand?
yes! i'm understanding it perfectly when it's in english but the second they bring out lawgic and conditionals and other nonsense, i get so confused. making me wonder if this is necesary for me to understand for the LSAT
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[deleted]
Wednesday, Jul 30, 2025
@partenr Apparently you need this stuff for complex problems, right? Because I agree with you that it makes sense in English then mathy logic makes it confusing, seems like I am tripping myself up on purpose.
You commented months ago, what did you find out knowing what you know now?
I'm not sure if I remember it being discussed in 7sage material, but I know that this is true because of a Logic class I took.
Yoda is an animal but Luke is a person.
If you take this sentence and break down the clauses (Yoda is an animal) and (Luke is a person), there is no "relationship" per se between the two of them. Not a disjunction, not a conditional, not a biconditional, all that makes sense is a conjunction relationship. In Logic, the sentence can be translated as Yoda is an animal and Luke is a person.
For those confused about uni-conditionals vs. bi-conditionals, consider these:
Uni-conditional example: "You will receive a medal if you finish the race in first-place."
We can logically create this diagram: finish race in first-place → receive a medal
Steve received a medal. Can we logically conclude that he therefore finished in first-place? No! The rule only tells us what happens if people finish first-place. Perhaps people who finished second and third also received a medal. Maybe every race participant received a medal! Who knows?
This makes so much more sense - and a good way to think about it in this example is if is a sufficient indicator and only if is a necessary indicator thus its both necessary and sufficient
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88 comments
does <-> just mean And? having still sufficient on left and necessary on right
@Oblivion I think it's to signal that the phrases are interchangeable. If Luke is a Jedi <-> then Yoda trained him. If Yoda trained Luke <-> then Luke is a Jedi.
#help Would it make sense if I say like sufficient is like enough for Luke to become a Jedi but there are other ways & for necessary it’s the only way required .
blue for luke green for yoda 😆
I really wish the time given in the study plan would at least correspond with the length of the video. The study plan claims this is a 2-minute section and the video is 6:49 long. Am I just supposed to ignore the video? This is happening frequently as I go through this study plan.
@thr107 Thanks for bringing this up -- we'll look into this. I think the plan is supposed to reflect the video time when there's a video, so if it's not, something's wonky.
clean version of my notes;
Here, we tackle a special category of conditional relationships: those in which two conditions are both sufficient and necessary for each other. What are Bi-Conditional Claims: They are just the conjunction of a uni-conditional claim and its converse.
Bi-Conditional Claims:
Luke will become a Jedi if Yoda trains him and Luke will become a Jedi only if Yoda trains him
Yoda’s training is sufficient and necessary for Luke becoming a Jedi.
Translating into Lawgic: (yoda - t → luke- j) (luke-j → yoda - t) [&]
Bi-Conditional in Lawgic: (yoda-t) ← (luke-j) it then looks like this (yoda-t ←→ luke-j)
So what does the bi-conditional mean? It means that Yoda’s training is sufficient and necessary for Luke becoming a Jedi.
The contrapositive of this will look like this: (/yoda-t ← → /luke - j)
Indicators for Bi-Condirionals:
If and only if
If but only of
Then and only then
Or…but not both
If…then…but not otherwise
Examples for Bi-Conditionals:
Luke will become a Jedi if and only if Yoda trains him
Luke will become a Jedi if but only if Yoda trains him
Luke will become a Jedi if Yoda trains him but not otherwise.
[These are all sufficient and necessary conditionals]
RECAP:
Uni-conditionals express sufficiency (Yoda’s training is sufficient for Luke to become a Jedi) or necessity (Yoda’s training is necessary for Luke to become a Jedi).
A bi-conditional indicates that the two conditions are both sufficient and necessary for each other (Yoda’s training is both sufficient and necessary for Luke to become a Jedi). They are mutually dependent. One occurs if and only if the other occurs.
Bi-conditionals claims are represented in Lawgic with the bi-conditional arrow: ← →
So then does it not matter which side of the arrow the conditions go on?
Would
Yoda-T <-> Luke-J and /Yoda-T <-> /Luke-J
still be correct?
@dylancameron814 didn’t even look at the lesson and it clicked because of your comment.
Wish they would have used this example:
Student are cited as late only if they arrive more than 5 minutes past home room bell.
Cited late-> 5+
John arrived 17 minutes past the home room bell. Can we logically assume John was cited as late? No. John got a note from his mommy.
Students are cited as late if and only if they arrive more than 5 minutes past homeroom bell.
Cited as late <—> 5+
John arrived more than 17 minutes late. Can we logically assume John received a citation? YES Your Tort professor will not accept notes from your mommy, or doctor or the psychiatrist you visited after finishing this lesson.
bi-conditionals are conditionals that drink matcha and listen to the cocteau twins
man, is law school worth this? i feel like just when I begin to get it, i don't get it.
@zee.marie you make me feel seen
@zee.marie don't worry diva you are preaching to a choir
What would a "Or... but not both" biconditional look like? Would we have to negate one of the given conditions for the Yoda example?
@caelesalad In short, yes. It is A <-> /B. It forces you to pick one and guarantees that if you pick one it will not be the other.
how long took you to come here at this lesson? for me 1 month
@Lidiia I am doing the advanced version of this because I am briefly going over foundations AGAIN. So, it's taken me a week and a half.
@Lidiia took me about 2.5 weeks. Everyone goes at their own pace though. More important to retain the information rather than just complete it.
It took me 4 days so far, might have to review again in the future but we'll see
Sounds like you just keep the sufficient?
Why can't you just drop the sufficient part of the bi-conditional?
@BradyWade That's basically what's happening. Any sufficient clause becomes necessary, both clauses necessitate the other.
Hey, I'm a bit confused about the classification here and would love some clarification!
I understand that a biconditional statement means 'If A then B, and if B then A'—so we can write it like:
A → B = ~A or B
B → A = ~B or A
A ↔ B = (~A or B) and (~B or A)
But I’m having trouble with how 7Sage classifies 'A or B, but not both' as a biconditional indicator. To me, it looks like 'A or B, but not both' is actually more like an exclusive-or (XOR), where it's one or the other, but not both.
For example, 'A or B, but not both' translates to:
(A or B) and ~(A and B) = (A or B) and (~A or ~B)
And that doesn't seem to match up with the biconditional logic, which is why I’m a little confused.
Am I missing something here? Or is there a specific context I’m not considering in how 7Sage is approaching this? I’d really appreciate any insight on this!
@LsatFootpad You're taking the logic of the uniconditional (testing the logic of its contrapositive) and applying it to the biconditional, which won't work. A biconditional is A and B, but not one or the other. Each clause of the biconditional is now sufficient and necessary for the other. They require each other to exist.
Example:
If raining, then cloudy.
If cloudy, then raining.
If it is raining, then it must be cloudy, and if it is cloudy then it must be raining.
It is raining if and only if it is cloudy.
It is cloudy if and only if it is raining.
R <-> C
Whereas if they are uniconditional, then it could be raining and not be cloudy (as seen in Hawaii often,) or it could be cloudy but not raining (as often the case in Seattle, though rain is common there as well.)
If biconditional, let's assume there is a fictional nation, Republic of Precipitation and Overcast Weather. Aptly named.
In this place, the biconditional exists where if it is cloudy then it is 100% raining outside no exception and vice versa, you won't get rain without clouds.
Hope that helps.
@dvo1d Thanks so much for the explanation! I think I’m starting to get it, but I’m still a bit unsure about how it relates to the original question.
The example you gave about 'If it’s raining, then it must be cloudy, and if it’s cloudy, then it must be raining' makes perfect sense to me as a biconditional: 'If and only if' one condition holds, the other one must hold as well.
However, when I look at the 'Or ... but not both' phrasing, it still seems more like an exclusive-or situation (XOR) to me. In other words, it’s either A or B, but not both at the same time—which feels more like the opposite of a biconditional.
For example, 'Cloudy or Raining, but not both' would work out to:
(Cloudy or Raining) and ~(Cloudy and Raining)
Which, when I compare it to the biconditional you used earlier, seems like a different structure entirely. That’s why I’m wondering if there’s something I’m missing about 7Sage’s interpretation of 'Or ... but not both' as a biconditional indicator. Could someone help me clarify this?
Thanks again for the help! I really appreciate it.
Luke will become a Jedi if Yoda trains him but not otherwise.
Yoda trains him --> Luke becomes a Jedi.
/Luke becomes a Jedi --> /Yoda trains him.
Is this the correct translation?
@Sameer_Ahamad the if...then...but not otherwise is an indicator for bi-conditionals meaning it can go either way, the specific lawgic translations you posted could go either way just ensure that both are positive or both are negative.
This clicked (sort of) for me by thinking of it as an exclusion of all other possible causes. In the case of the example sentence, the ONLY path that Luke has to become a Jedi is via being trained by Yoda, and being trained by Yoda is CERTAIN to make him a Jedi.
Therefore, you can derive information in both directions. If Yoda DOES train him then he will become a Jedi. If he DOES become a Jedi Yoda must have trained him.
This is different from typical logical relations where you are limited in what you can know. For example:
if A -> B, the contrapositive is /B -> /A
If we are given information about /A, we do not know what happens in this case because there is no arrow flowing from it to another thing (to egregiously oversimplify the actual mechanism). But if instead we had:
A <-> B and its contrapositive /A <-> /B
We now know what /A causes, it must mean cause /B, whereas in the first case you would not be able to generate any reliable conclusions.
If two events are inextricably linked, and are the sole causes of one another, the "if and only if" wording applies, and you have this certainty that if one event happens, the other MUST as well (no matter which you start from). This logic also applies after negation.
imma bout to crash out
dyinggg here
real
In my opinion the best way to explain/understand a bi-conditional claim is how it is taught in Math. It is taught as an 'iff' claim aka. an if and only if claim.
All an iff claim means is that each element implies the other:
Iff A then B, means: A --> B, and B --> A.
It is helpful to differentiate an iff claim from a regular conditional because of LSAT questions as so:
an animal is a zebra if and only if it has white and black stripes. (our biconditional claim in an argument on the LSAT)
Jerry is an animal that has black and white stripes. (an assertion made as part of the argument)
What inference can you make? (LR question on LSAT)
That Jerry is a zebra. (Answer derived by understanding that it is an iff claim, so both elements imply each other)
@sakinasohail01555IThanks for this
Starting to feel a little excessive
my brain is fried, everything after the kick it up lesson is just mad confusing
so valid
@naomiy2k I feel the same way, but honestly, as you move forward I feel like the information starts to subconsciously make sense and you start to apply what you've learnt without necessarily digging deep into the trenches of you brain lol
@naomiy2k To my understanding the kick it up method is not something you need to use when evaluating a conditional claim, but is an option that makes it easier. At the moment I generally have not been thinking about it in drills but I think I eventually will when I train harder levels.
I don't quite understand why "or....but not both" would an indicator for bi-conditionals
Luke becomes a Jedi or Yoda does not train him but not both.
This is saying the same thing as: Luke becomes a Jedi if and only if Yoda trains him.
@mariafreese You are negating the one of the conditions here though.
A or B but not both is not the same as A or not B, but not both.
Is it the case for anyone else that you understand how to work out these scenarios in English, but the Lawgic translation then makes it confusing to understand?
yes! i'm understanding it perfectly when it's in english but the second they bring out lawgic and conditionals and other nonsense, i get so confused. making me wonder if this is necesary for me to understand for the LSAT
@partenr Apparently you need this stuff for complex problems, right? Because I agree with you that it makes sense in English then mathy logic makes it confusing, seems like I am tripping myself up on purpose.
You commented months ago, what did you find out knowing what you know now?
when was BUT described as a conjunction?
I'm not sure if I remember it being discussed in 7sage material, but I know that this is true because of a Logic class I took.
Yoda is an animal but Luke is a person.
If you take this sentence and break down the clauses (Yoda is an animal) and (Luke is a person), there is no "relationship" per se between the two of them. Not a disjunction, not a conditional, not a biconditional, all that makes sense is a conjunction relationship. In Logic, the sentence can be translated as Yoda is an animal and Luke is a person.
@rachelwallis1238 there was a lesson about it a little after the conjunction lesson.
For those confused about uni-conditionals vs. bi-conditionals, consider these:
Uni-conditional example: "You will receive a medal if you finish the race in first-place."
We can logically create this diagram: finish race in first-place → receive a medal
Steve received a medal. Can we logically conclude that he therefore finished in first-place? No! The rule only tells us what happens if people finish first-place. Perhaps people who finished second and third also received a medal. Maybe every race participant received a medal! Who knows?
----------------------------------------------------------------
However, consider this bi-conditional example:
"You will receive a medal if and only if you finish the race in first-place."
The arrows now point both ways: finish in first place ↔ receive a medal
Christopher received a medal. Can we therefore logically conclude that he finished in first place? Yes!
(likewise, if we were just told that Christopher "finished in first-place," we could also logically conclude that he therefore received a medal).
This makes so much more sense - and a good way to think about it in this example is if is a sufficient indicator and only if is a necessary indicator thus its both necessary and sufficient
Good example, thanks!
Thank you for this
This is how I understand but not otherwise:
Basically stating not the sentence right before it.
For example
If Yoda trains him, Luke will become a Jedi
Otherwise
If Yoda does not train him, Luke will not become a Jedi