If these last several lessons are ever updated, it would be so helpful if you could replace the "A"s and "B"s in the Lawgic write-ups with the actual example being used (ie Harry Potter friends/wizards or Jedi/Force, etc.). It would make following along and comparing our own work much easier.
Ok so I was a bit confused on this example until I honestly dropped the Lawgic and just used my intuition.....
So the statement reads: "Most classically trained opera singers can recite the lyrics to Musetta's Waltz and most people who have not received such training cannot. It seems likely, therefore, that Anna, who can recite the lyrics to Musetta's Waltz, was classically trained."
Lets break it down though, basically the part that says "most classically trained opera singers can recite the lyrics to Musetta's Waltz" is sayin that of all the classically trained opera singers in the world, most of them can recite the lyrics to Musetta's Waltz. And intuitively this makes sense, because as people who are classically trained, you'd expect that most of them know the lyrics to Musetta's Waltz.... or in other words, you'd expect someone in that field to know about the music within their field.
Now let's look at the next part..." most people who have not received such training cannot."
Ok, so this is saying that if you are not one of those people who is a classically trained opera singer, then you probably cannot recite the lyrics to Musetta's Waltz. And honestly, this makes sense because, for example, I am not someone who is a classically trained opera singer and I cannot recite Musetta's Waltz lyrics to you if you asked lolll. And tbh if you asked my friends who are also not classically trained opera singers, they most definitely would not be able to recite the lyrics either. But that's just me and my friends, not the whole world. It's entirely possible, and very likely, that there are people in the world who, like my friends and I, are not classically trained opera singers but CAN recite the lyrics to Musetta's Waltz.
That being said, if we take the last sentence, "It seems likely, therefore, that Anna, who can recite the lyrics to Musetta's Waltz, was classically trained." it is not valid because the writer is making a HUGE assumption.
They are saying that because Anna can recite the lyrics to Musetta's Waltz she must have been classically trained. But that's just not true. What if Anna is just one of those people in the world who is not a classically trained person but can recite the lyrics? It is entirely possible that Anna can recite Musetta's lyrics simply because she heard it, idk, on the radio or something and now she can recite it.
Thus, the statement at the end is a false implication. I hope I didn't confuse anyone further, but this is how I broke it down in my head, so hopefully this helps someone lol.
I had the same thought process as yours. I am just concerned that it is a good technique for the actual exam because it will be stated in more complex terms. I cannot grasp the concept in the LAWGIC terms like A --> B.
this is the best explanation I have seen for it and this is how I used my intuition on this one. I know that lawgic may be important but this realist approach to breaking it down is the best way for anyone to understand.
“Most of Harry Potter's friends are wizards. Most people who are not his friends are not wizards. Therefore, Draco Malfoy, who is a wizard, is probably Harry Potter's friend.”
P1: Friends ‑m→ Wizards
P2: /Friends ‑m→ /Wizards
BUT don't confuse this. You cannot take the counter positive of "most" arguments. They will ALWAYS BE INVALID.
Wizards -m --> Friends
This says... Most wizards are Harry's friends...
Wizards are a BIGGER group than Harry's friends. It's absurd then, to think that most of the wizarding world is Harry's friends.
C: Draco Malfoy (Wizard) → Friend (FALSE)
This is invalid...because in the first premise most of Harry's friends are wizards. The conclusion confuses sufficiency for necessity.
Just because Malfoy is a wizard doesn't mean he is Harry's friend! In the first premise we cannot switch the sufficient condition and the necessary condition It is the same for the 2nd premise as well.
The conclusion is false because those conditions aren't met by the premises.
Most classically trained opera singers can recite the lyrics to Musetta's Waltz and most people who have not received such training cannot. It seems likely, therefore, that Anna, who can recite the lyrics to Musetta's Waltz, was classically trained.
CTOS = classically trained opera singers
RLMW = can recite the lyrics to Musseta's Waltz
/CTOS = Most people who have not received such training ("such training" is a referential for "classically trained opera singers")
/RLMW = cannot (another referential. This time it refers to "recite the lyrics to Musseta's Waltz", negating it.)
A= Anna
So the Lawgic translation is:
CTOS ‑m→ RLMW
/CTOS ‑m→ /RLMW
A RLMW
---------------------
A CTOS
This is invalid because it's reading the ‑m→ arrow backwards as RLMW ‑m→ CTOS when it is the other way around.
For the conclusion to be valid it would've had to read "It seems likely, therefore, that Anna, who was classically trained, can recite the lyrics to Musetta's Waltz."
Someone said this on the previous lesson in this series, however I think it would be a lot more helpful to use A and B in the sentences or when writing out the Lawgic putting representative letters.
If someone is already confused on what about the structure is correct/incorrect, not clearly being able to define what each term represents makes the explanation significantly more difficult #feedback
Hello, Mary! It would be great if in this lessons and the previous ones the terms for logic were representative of the statements, not just A and B. I've seen several people comment this. Thanks!
This one is so confusing. Sometimes you're supposed to only use information that the passage gives you, but at other times using outside knowledge is needed...
@xyzana YES. sometimes using your intuition is a better tool than mapping it out. These modules are just other tools that can help prevent you from confusing sufficiency and necessity, because most times on the test your intuition may not help. These are good to rely on when all else fails.
The way that I thought about the opera example in my own terms:
Most NBA players can dunk a basketball, and most people who are not NBA players cannot. Therefore, it seems likely that since I can dunk, I play in the NBA.
1- There are very few NBA players in the world. Just because I can dunk doesn't offset the very low statistical probability that I am an NBA player.
2- There are plenty of other people who can dunk but are not in the NBA (e.g. college basketball players or retired NBA players).
@isabellagirjikian I actually feel like we lowkey already learned these in video format. Reading it is kind of like reaffirming it in a new context. The effort even might help the material to stick more, especially since it is partially review! 👍🏻
the fact that this entire unit has zero videos is really pissing me off. I paid for a course with videos and instruction, not examples I could ask AI to do for me for free lol.
To understand that the conclusion in the second example is invalid, (Anna is classically trained), we just have to look at the word most.
From the lessons about the quantifier "most", we know that "most" can include "all", but not always. In this example, saying that Anna was classically trained because she can recite Musetta's Waltz is erroneous.
The example assumes that only classically trained opera singers can recite Musetta's Waltz and that people who are not classically trained cannot recite Musetta's Waltz. However, the example said most, not all.
By following these assumptions, the example also made the error of confusing necessity with sufficiency by saying that her ability to recite is a sufficient condition for her being classically trained.
If this example followed the assumption they made in the conclusion, the lawgic would be:
classically-trained --> recite
/classically-trained --> /recite
NOT
recite --> classically-trained
/recite --> /classically trained
As a whole, however, we cannot validate whether Anna was classically trained because we only know that the majority of classically trained opera singers can recite Musetta's Waltz and the majority can’t. Anna may be classically trained, but she also could be the large minority of un-trained people in the world who can recite it. The correct lawgic is:
Helpful, thank you. One thing I'm wondering about is if the validity changes if we were to say "the overwhelming majority of people who have not received such classical training cannot recite Musetta's Walz". I assume it's still invalid, but brings us closer to the intuitive answer that if you meet someone who can recite an obscure classical piece they likely received some classical training. thoughts?
The opera one is tough because it says "likely", which I would think is something you can say from the information in the premises. "Likely" doesn't mean "we can conclude she is classically trained", its more so "given this information its probable that she is classically trained", which leaves room to still conclude, "she is not classically trained". On the test, I would probably get this wrong because "it seems likely" does a lot of work to make the conclusion make sense.
@sillybillyblu Yes, I think, so long as Harry has any friends at all. "Some" implies that at least one wizard is his friend. If the majority of his friends are wizards, then at least one wizard is Harry's friend.
You could just imagine "most" as being a more descriptive version of "some". So it's like saying "some of HP's friends are wizards. Therefore some wizards are HP's friend." Some arrows are reversible.
@sillybillyblu This should work like if Harry has 10 friends, more than 5 of whom are wizards.
Some Wizards are his friends; it is just saying at LEAST one, possibly all, wizards are his friends. The main thing we are guaranteeing is that at least one wizard is his friend, which is true based on the premises.
117 comments
If these last several lessons are ever updated, it would be so helpful if you could replace the "A"s and "B"s in the Lawgic write-ups with the actual example being used (ie Harry Potter friends/wizards or Jedi/Force, etc.). It would make following along and comparing our own work much easier.
seriously agree #feedback
Ok so I was a bit confused on this example until I honestly dropped the Lawgic and just used my intuition.....
So the statement reads: "Most classically trained opera singers can recite the lyrics to Musetta's Waltz and most people who have not received such training cannot. It seems likely, therefore, that Anna, who can recite the lyrics to Musetta's Waltz, was classically trained."
Lets break it down though, basically the part that says "most classically trained opera singers can recite the lyrics to Musetta's Waltz" is sayin that of all the classically trained opera singers in the world, most of them can recite the lyrics to Musetta's Waltz. And intuitively this makes sense, because as people who are classically trained, you'd expect that most of them know the lyrics to Musetta's Waltz.... or in other words, you'd expect someone in that field to know about the music within their field.
Now let's look at the next part..." most people who have not received such training cannot."
Ok, so this is saying that if you are not one of those people who is a classically trained opera singer, then you probably cannot recite the lyrics to Musetta's Waltz. And honestly, this makes sense because, for example, I am not someone who is a classically trained opera singer and I cannot recite Musetta's Waltz lyrics to you if you asked lolll. And tbh if you asked my friends who are also not classically trained opera singers, they most definitely would not be able to recite the lyrics either. But that's just me and my friends, not the whole world. It's entirely possible, and very likely, that there are people in the world who, like my friends and I, are not classically trained opera singers but CAN recite the lyrics to Musetta's Waltz.
That being said, if we take the last sentence, "It seems likely, therefore, that Anna, who can recite the lyrics to Musetta's Waltz, was classically trained." it is not valid because the writer is making a HUGE assumption.
They are saying that because Anna can recite the lyrics to Musetta's Waltz she must have been classically trained. But that's just not true. What if Anna is just one of those people in the world who is not a classically trained person but can recite the lyrics? It is entirely possible that Anna can recite Musetta's lyrics simply because she heard it, idk, on the radio or something and now she can recite it.
Thus, the statement at the end is a false implication. I hope I didn't confuse anyone further, but this is how I broke it down in my head, so hopefully this helps someone lol.
This helped so much!!!!!
I had the same thought process as yours. I am just concerned that it is a good technique for the actual exam because it will be stated in more complex terms. I cannot grasp the concept in the LAWGIC terms like A --> B.
Literally saved me. The Lawgic is only helpful to me when I am trying to set up a basic understanding of the question
this is the best explanation I have seen for it and this is how I used my intuition on this one. I know that lawgic may be important but this realist approach to breaking it down is the best way for anyone to understand.
It's typically called the base rate fallacy for those who'd like to Google more examples.
@cheetah123 YES! This was great wrap up of what they're trying to get to us
For the last example...for those WHO NEED HELP:
“Most of Harry Potter's friends are wizards. Most people who are not his friends are not wizards. Therefore, Draco Malfoy, who is a wizard, is probably Harry Potter's friend.”
P1: Friends ‑m→ Wizards
P2: /Friends ‑m→ /Wizards
BUT don't confuse this. You cannot take the counter positive of "most" arguments. They will ALWAYS BE INVALID.
Wizards -m --> Friends
This says... Most wizards are Harry's friends...
Wizards are a BIGGER group than Harry's friends. It's absurd then, to think that most of the wizarding world is Harry's friends.
C: Draco Malfoy (Wizard) → Friend (FALSE)
This is invalid...because in the first premise most of Harry's friends are wizards. The conclusion confuses sufficiency for necessity.
Just because Malfoy is a wizard doesn't mean he is Harry's friend! In the first premise we cannot switch the sufficient condition and the necessary condition It is the same for the 2nd premise as well.
The conclusion is false because those conditions aren't met by the premises.
@OmarAbuaita Thanks for this
Most of the food I eat is Cheetos, therefore most of the Cheetos that exist are eaten by me.
what happened to the video explanations lol
Most classically trained opera singers can recite the lyrics to Musetta's Waltz and most people who have not received such training cannot. It seems likely, therefore, that Anna, who can recite the lyrics to Musetta's Waltz, was classically trained.
CTOS = classically trained opera singers
RLMW = can recite the lyrics to Musseta's Waltz
/CTOS = Most people who have not received such training ("such training" is a referential for "classically trained opera singers")
/RLMW = cannot (another referential. This time it refers to "recite the lyrics to Musseta's Waltz", negating it.)
A= Anna
So the Lawgic translation is:
CTOS ‑m→ RLMW
/CTOS ‑m→ /RLMW
A RLMW
---------------------
A CTOS
This is invalid because it's reading the ‑m→ arrow backwards as RLMW ‑m→ CTOS when it is the other way around.
For the conclusion to be valid it would've had to read "It seems likely, therefore, that Anna, who was classically trained, can recite the lyrics to Musetta's Waltz."
Thank you!
Back again with another explanation in hopes of it helping you because it might help me.
The key take away here: Don't read unidirectional arrows backwards
Just because most A are B, does not mean most B are A
Example:
Most of the water I drink is freshwater. Therefore, most freshwater is drank by me.
Lawgic:
Water I drink -m-> Freshwater
-----
Freshwater -m-> Drank by me
Is this valid? Does the premise being true make the conclusion true? NO! THIS IS INVALID.
Just because most of the water I drink is freshwater, DOES NOT MEAN that most of the freshwater is drank by me.
Just because most A are B, DOES NOT MEAN most B are A.
Someone said this on the previous lesson in this series, however I think it would be a lot more helpful to use A and B in the sentences or when writing out the Lawgic putting representative letters.
If someone is already confused on what about the structure is correct/incorrect, not clearly being able to define what each term represents makes the explanation significantly more difficult #feedback
Hi there,
Thanks for your valuable feedback! We are constantly improving, so every feedback will help us improve. I will make sure to share this with our team.
Please let me know if you have any concerns. I'm happy to help!
Hello, Mary! It would be great if in this lessons and the previous ones the terms for logic were representative of the statements, not just A and B. I've seen several people comment this. Thanks!
I second this!
This one is so confusing. Sometimes you're supposed to only use information that the passage gives you, but at other times using outside knowledge is needed...
I wish they had videos for these lessons. I'm wasting way too much time trying to confirm if I got the examples right. This is so annoying.
It makes sense to me at first, but then when I try to apply Lawgic to explain it, I start to confuse myself lol
naaah the opera singer example isn't making any sense.
I think it is still the same as confusing sufficiency and necessity.
A - m -->B
A is the sufficient condition for B in the sense that when most of A happens, B happens.
But
it does NOT mean that when most of B happens, A happens.
Example:
Most of my friends are lawyers. Therefore, most of the lawyers are my friends.
my friends - m --> lawyers.
--------------------------------
lawyers - m --> my friends
Invalid!!!!!
I wish most of lawyers were my friends though lols
[This comment was deleted.]
@xyzana YES. sometimes using your intuition is a better tool than mapping it out. These modules are just other tools that can help prevent you from confusing sufficiency and necessity, because most times on the test your intuition may not help. These are good to rely on when all else fails.
The way that I thought about the opera example in my own terms:
Most NBA players can dunk a basketball, and most people who are not NBA players cannot. Therefore, it seems likely that since I can dunk, I play in the NBA.
1- There are very few NBA players in the world. Just because I can dunk doesn't offset the very low statistical probability that I am an NBA player.
2- There are plenty of other people who can dunk but are not in the NBA (e.g. college basketball players or retired NBA players).
is there a video? what is the opera singer argument?
where are the videos for these? :/
@isabellagirjikian I actually feel like we lowkey already learned these in video format. Reading it is kind of like reaffirming it in a new context. The effort even might help the material to stick more, especially since it is partially review! 👍🏻
the fact that this entire unit has zero videos is really pissing me off. I paid for a course with videos and instruction, not examples I could ask AI to do for me for free lol.
#feedback
How do we deal with "probably" claims, like in the opera example?
#feedback It might be helpful to put quotation marks around "Most" in the title of this page
Agreed. Took me a second to realize they weren't making a general statement, but were talking about 'most' as a lawgic relationship.
To understand that the conclusion in the second example is invalid, (Anna is classically trained), we just have to look at the word most.
From the lessons about the quantifier "most", we know that "most" can include "all", but not always. In this example, saying that Anna was classically trained because she can recite Musetta's Waltz is erroneous.
The example assumes that only classically trained opera singers can recite Musetta's Waltz and that people who are not classically trained cannot recite Musetta's Waltz. However, the example said most, not all.
By following these assumptions, the example also made the error of confusing necessity with sufficiency by saying that her ability to recite is a sufficient condition for her being classically trained.
If this example followed the assumption they made in the conclusion, the lawgic would be:
classically-trained --> recite
/classically-trained --> /recite
NOT
recite --> classically-trained
/recite --> /classically trained
As a whole, however, we cannot validate whether Anna was classically trained because we only know that the majority of classically trained opera singers can recite Musetta's Waltz and the majority can’t. Anna may be classically trained, but she also could be the large minority of un-trained people in the world who can recite it. The correct lawgic is:
classically-trained --m--> recite
/classically-trained --m--> /recite
Helpful, thank you. One thing I'm wondering about is if the validity changes if we were to say "the overwhelming majority of people who have not received such classical training cannot recite Musetta's Walz". I assume it's still invalid, but brings us closer to the intuitive answer that if you meet someone who can recite an obscure classical piece they likely received some classical training. thoughts?
What has been helpful for me to understand these various logic flaws is visualizing by drawing circles
The opera one is tough because it says "likely", which I would think is something you can say from the information in the premises. "Likely" doesn't mean "we can conclude she is classically trained", its more so "given this information its probable that she is classically trained", which leaves room to still conclude, "she is not classically trained". On the test, I would probably get this wrong because "it seems likely" does a lot of work to make the conclusion make sense.
For the HP argument, can I say that most of Harry Potter's friends are wizards. Therefore, some wizards are Harry Potter's friends. Is that valid?
How would it be written out?
@sillybillyblu Yes, I think, so long as Harry has any friends at all. "Some" implies that at least one wizard is his friend. If the majority of his friends are wizards, then at least one wizard is Harry's friend.
You could just imagine "most" as being a more descriptive version of "some". So it's like saying "some of HP's friends are wizards. Therefore some wizards are HP's friend." Some arrows are reversible.
@chris.eveland0 Bet thanks!!
@sillybillyblu This should work like if Harry has 10 friends, more than 5 of whom are wizards.
Some Wizards are his friends; it is just saying at LEAST one, possibly all, wizards are his friends. The main thing we are guaranteeing is that at least one wizard is his friend, which is true based on the premises.
Draco Malfoy being in my LSAT modules was not on my 2026 bingo card