Does this mean this is the strongest type of argument because there is only one path to achieving the necessary condition? No wiggle room for other assumptions? I'm thinking about our sufficient and necessary circles being one and the same vs concentric. Am I off base / thinking about this incorrectly?
It pouring is necessary and sufficient for it raining, it raining is necessary and sufficient for it pouring, they are mutually exclusive. If one happens then the other one happens, if one does not happen the other does not happen!
im confused. doesnt "if and only if" mean just necessary not sufficient? saying luke will become a jedi if and only if Yoda Trains him would mean that Yoda's training is necessary for luke to become a jedi. But how would it also be sufficient? Seems only necessary to me
@Arsalan06 the if before AND [IF and only if] is part of the first uni-conditional that is being joined by the conjunction and. so if you were to parse this sentence, it would be, luke will become a jedi if yoda trains him. then the next sentence would come after the AND [if and ONLY IF], luke will become a jedi only if yoda trains him. we're just shortening two sentences and joining them together by using a conjunction. hence, sufficient and necessary! :)
I seem to be missing something here.. What is the difference between ( Yoda's training -> Luke becoming a Jedi) and ( Yoda's training <-> Luke becoming a Jedi) .. In both cases Yoda's training leads to luke becoming a Jedi right?
@GradyGaunt I think the difference is that with the <-> Luke becoming a jedi means that Yoda trained him. Without the <->, Luke could become a Jedi if someone else trained him. So yes, the training in both cases does lead to him becoming a jedi, it is only the matter of if it is the only way.
Oh yeah, this is when the fun begins. Only thing you can do is to keep pressing forward. Sometimes you have to mess up applying these concepts in order for them to click. Don't get stuck here, keep going and keep failing: that's how you learn!! Don't give up :D
@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.
104 comments
Does this mean this is the strongest type of argument because there is only one path to achieving the necessary condition? No wiggle room for other assumptions? I'm thinking about our sufficient and necessary circles being one and the same vs concentric. Am I off base / thinking about this incorrectly?
Example of a bi-conditional:
If it rains it pours
Rains->pours
It pours only if it rains
pours->rains
It pours if and only if it rains
Pours<->rains
It pouring is necessary and sufficient for it raining, it raining is necessary and sufficient for it pouring, they are mutually exclusive. If one happens then the other one happens, if one does not happen the other does not happen!
just out of curiosity, can we not say bi-conditional is just a chain condition with a looping back scenario to where we started?
Yoda-t → Luke-j → Yoda-t
For the contrapositive version: Why, in uni-conditions, we flip and negate both, but in bi-conditions, we don't flip the claims?
Just got back into studying for the LSAT after taking a 3-month break. Will be taking the test in November. Wish me luck!
@marikitten03 GOOD LUCK!
im confused. doesnt "if and only if" mean just necessary not sufficient? saying luke will become a jedi if and only if Yoda Trains him would mean that Yoda's training is necessary for luke to become a jedi. But how would it also be sufficient? Seems only necessary to me
@Arsalan06 the if before AND [IF and only if] is part of the first uni-conditional that is being joined by the conjunction and. so if you were to parse this sentence, it would be, luke will become a jedi if yoda trains him. then the next sentence would come after the AND [if and ONLY IF], luke will become a jedi only if yoda trains him. we're just shortening two sentences and joining them together by using a conjunction. hence, sufficient and necessary! :)
So instead of a big circle and a small circle, would this be represented as just one circle?
I seem to be missing something here.. What is the difference between ( Yoda's training -> Luke becoming a Jedi) and ( Yoda's training <-> Luke becoming a Jedi) .. In both cases Yoda's training leads to luke becoming a Jedi right?
@GradyGaunt I think the difference is that with the <-> Luke becoming a jedi means that Yoda trained him. Without the <->, Luke could become a Jedi if someone else trained him. So yes, the training in both cases does lead to him becoming a jedi, it is only the matter of if it is the only way.
Oh yeah, this is when the fun begins. Only thing you can do is to keep pressing forward. Sometimes you have to mess up applying these concepts in order for them to click. Don't get stuck here, keep going and keep failing: that's how you learn!! Don't give up :D
@RubemSantos Love this
@petvma Thanks. I hope you're fairing well with your studies.
Okay, basically Yoda's training is necessary and guarantees that Luke will become a Jedi ?
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
@zee.marie preach
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.