Hi all, I made another flashcard set. This time for memorizing Quantifiers. Flashcards are what really helped me in undergrad and so I decided to make them to companion my 7sage studies. Thought I'd share to help others who would benefit :) made a folder that I will most likely add more sets to as I go. Much Love and happy studying! https://quizlet.com/user/ehoffmanwallace/folders/lsat-7sage-flashcards
To negate "All dogs are friendly," we'd be focusing on the word "all" and disproving that specific word by saying, "It is not true that all dogs are friendly." This negated statement logically states that, at the very least, there exists at least one dog that is not friendly; hence, the existence of at least one unfriendly dog means that it's impossible for every single dog in existence to be friendly.
Going back a few lessons, we also know that "some" entails a numerical baseline of at least one. Therefore, this negated statement could also be written as, "Some dogs are not friendly." That's why the negation of "All dogs are friendly," is "Some dogs are not friendly!"
Good luck in your studies! Trust your gut and intuition, and reward yourself for every little bit of progress you make!!
@KoviFried Let me use an example, hopefully this clears something up.
statement: some LSAT studiers are full-time students.
If I say that all LSAT students are full-time students, it still means that some are (because some is at least one).
statement: all LSAT studiers are full-time students.
If I say this, it can't mean SOME are full-time students, because it would have to mean that 100% of studiers are full-time students, not just one. The upper boundary for all is 100%, whereas some is a bit more nebulous.
If a hot-dog cart had 10 hot-dogs and you said you wanted all of them and they only gave you five, you'd be pretty annoyed, right? But if you said you wanted some hot dogs and they gave you all ten, your request would still technically be satisfied, as some is more than one (and 10 is more than one, which happens to be all in this case).
I hope that helped! If that made it more confusing, I can clear it up.
All A are B. To negate this claim we must deny the relationship, not the existence of a set. The way we think about this relationship is the quality of being "all". To deny the relationship, we would say some As are not B.
All jackfruit is splendid. J->S
Negated: J <-s->/S meaning some jackfruits are not splendid.
I understand that A ←s→ /B is the negation of A → B.
However, given that the meaning of 'some' is 'at least one, possibly all', does that mean that there is a possibility for A ←s→ /B to become A → /B as the negation of A → B?
I think they are using the "some are not" B to implicitly show that ALL of A is NOT B. if you say all of A --> /B then, you are saying it is never possible. However, if we had just one A that is not B then it would work for the A ←s→ /B. For EXAMple, the UC Berkeley students live in Berkeley. And then we find out that one student moves to Oakland. Then we have some students who are not living in Berkeley. If you used the A--> /B then it would reflect that none of these students live in Berekely. I'm sorry if I explained this wrong, I gave it my best shot.
@GDatria715 I just take it as them saying it shouldn’t be the default.
In a real life situation, if I’m saying “not all” then the first assumption is “some”.
Let’s say you’re having a party and you invite 100 people. Someone asks you if every one coming to the party and you say, no not all. Most people will then follow up with: “Oh okay. Well, how many people are coming?” So it’s like the default in real life is “some” and while it COULD be “none”, the LSAT will try to trick you if you default to that.
@GDatria715 you’re missing the core meaning in all of this.
If we have the statement: all dogs are friendly. The negated statement (proving the statement false) is just saying this: some (from 1-100%) dogs are not friendly.
It could be all dogs aren’t friendly or only 1 dog in the universe is not friendly. We can’t infer from the original statement. The some in the negated sentence spans the entire potential cases for which you could negate the original statement.
@Luna Yes I believe so. "Its not the case that all dogs are friendly" denies that all dogs are friendly. This translates to "some dogs are not friendly".
To me it's confusing to include /(D -> F) because in algebra, you would distribute whatever is outside of the parenthesis and get /D -> /F. But in Lawgic, it really means to negate the necessary condition to create a condition that contradicts the original claim. And you can't contradict the original claim without having the non-negated sufficient condition. If you negate the sufficient condition, then you are talking about a different scenario than the one you're trying to negate. That's how I'm interpreting these lessons, let me know if I have anything wrong though
@Tannercho06897 Contrapositive and negation are different!
Contrapositive is an equivalent way of expressing the relationship. We typically create a contrapositive of a normal conditional relationship (ex. cats are mammals) by flipping sufficient and necessary conditions, and negating each condition (ex. if not a mammal, then not a cat). These are two ways of expressing the same relationship.
Negation of an All statement/relationship ("it is not the case that all ...") is creating the opposite of the relationship. For example, the negation of "all cats are mammals" would be "some cats are not mammals". They express totally different relationships between the sets.
@ckilk I am struggling with this distinction too. How do I know that the statement "all dogs are friendly" is not a conditional? My instinct was to put it into lawgic as "if dog --> friendly" and "/friendly --> /dog." Why can't I do that? Thanks!
@Hashibiro You can treat "all dogs are friendly" as "if dog --> friendly"! But, when you negate that whole relationship you want to turn it into "not all dogs are friendly" or "some dogs are not friendly".
To say "/friendly --> /dog" means "if it is not friendly, then it is not a dog" which is the same as saying "all dogs are friendly" . So you've just written "if dog --> friendly" in an equivalent way that expresses the same idea (the contrapositive). This chapter is about negating a whole Statement saying that "it is not the case that Statement is true"
@ArthurMorgan Good point! I guess this depends on the subtleties of your interpretation of the word "opposite". I just wanted to use a term other than "negate" and it made sense to me. :)
If you see the "opposite" of "left" to be "right", then "opposite" is probably not a good term to use for your personal understanding because as you said, this is not the same as negating.
If you see the "opposite" of "left" to be "not left" (which could be straight or really any other direction that is not left), then you're probably in the same frame of mind I was when I wrote my OG comment
So the difference between the contrapositive and the negation of a claim is that contrapositive reverses and negates to be logically equal to original. Negation of a claim means creating a contradictory statement.
Example : if it rains the ground is wet
R--> G
contrapositive: if the ground is not wet, it did not rain
@PranjalChaudhary Not most, but some. We don't know what percentage of the A group that is not B. Most means more than half. It could just be one A that is not B, and some encompasses that range.
So, in this lesson we're learning how to negate a relationship, but previously we were negating conditions/logic? I'm a bit confused on how to put into words the difference between
A->B
/B->/A
and this new process that goes:
A->B
AB
If the indicator word is "all", how do you know whether to take the negation of the sufficient condition or this new negation process for "some"? Or does it boil down to what the question stem asks? Thanks in advance for any help, I'm a bit too confused to explain what exactly is confusing me...
So you're talking about two different concepts that visually look similar.
Contrapostive: Rephrasing of conditional statement that does NOT deny it.
Negation: Denying the conditional statement.
We'll use an example to flesh these two out.
Conditional Logic: A > B
Every instance of A there is B.
Contrapostive: /B > /A
Every instance of not B there is no A. Logically the exact same as the original statement.)
Negation: /(A > B)
Not every instance of A will there be B.
Negation: A <s> /B
At least one instance of A there is not B (some lower boundary is one).
How is this applicable? Off the top of my head you get some passage about how A > B but the auther disagrees with this conditional statement being true. Then you're given this question stem:
"Which of the following most strongly supported by the statements in the stimulus?"
Most instance of A there B may not appear
When B is not happening, then A would appear.
Every instance of A is not B.
There is at least once instance of A where it's not B. (correct answer)
This is a bit straight forward, and of course it's spelled out for you this way, but, it should give you a rough idea of what may appear.
Couldn't we just say "not all dogs are friendly" in order to negate "all dogs are friendly"? Is there a difference between "not all dogs are friendly" and "some dogs are not friendly"?
Yes, it's the same thing as saying "it's not the case that all dogs are friendly" which also means "some dogs are not friendly" because they are not in the intersection between the "dogs" set and the "friendly (beings)" set, therefore, they are "not friendly"
133 comments
Do not confuse this with the creation of contrapositives which are logically equivalent to the original statement.
Hi all, I made another flashcard set. This time for memorizing Quantifiers. Flashcards are what really helped me in undergrad and so I decided to make them to companion my 7sage studies. Thought I'd share to help others who would benefit :) made a folder that I will most likely add more sets to as I go. Much Love and happy studying! https://quizlet.com/user/ehoffmanwallace/folders/lsat-7sage-flashcards
Can we also negate "All dogs are friendly" by simply writing "Not all dogs are friendly"?
yes
To negate "All dogs are friendly," we'd be focusing on the word "all" and disproving that specific word by saying, "It is not true that all dogs are friendly." This negated statement logically states that, at the very least, there exists at least one dog that is not friendly; hence, the existence of at least one unfriendly dog means that it's impossible for every single dog in existence to be friendly.
Going back a few lessons, we also know that "some" entails a numerical baseline of at least one. Therefore, this negated statement could also be written as, "Some dogs are not friendly." That's why the negation of "All dogs are friendly," is "Some dogs are not friendly!"
Good luck in your studies! Trust your gut and intuition, and reward yourself for every little bit of progress you make!!
Arbys
@JDMurphy get this man some arbys
To negate:
All --> 99%
Most --> 49%
Some --> 0
None --> 1
Where would we use this idea of negating "all"? Like what question type on the lsat?
How can not all mean some if some can mean all?
@KoviFried Let me use an example, hopefully this clears something up.
statement: some LSAT studiers are full-time students.
If I say that all LSAT students are full-time students, it still means that some are (because some is at least one).
statement: all LSAT studiers are full-time students.
If I say this, it can't mean SOME are full-time students, because it would have to mean that 100% of studiers are full-time students, not just one. The upper boundary for all is 100%, whereas some is a bit more nebulous.
If a hot-dog cart had 10 hot-dogs and you said you wanted all of them and they only gave you five, you'd be pretty annoyed, right? But if you said you wanted some hot dogs and they gave you all ten, your request would still technically be satisfied, as some is more than one (and 10 is more than one, which happens to be all in this case).
I hope that helped! If that made it more confusing, I can clear it up.
@kyorofan20 that helped a lot, thank you
can't we also just say that "all dogs are friendly" negated is "not all dogs are friendly"?
I think not all is logically equivalent to some are not.
All A are B. To negate this claim we must deny the relationship, not the existence of a set. The way we think about this relationship is the quality of being "all". To deny the relationship, we would say some As are not B.
All jackfruit is splendid. J->S
Negated: J <-s->/S meaning some jackfruits are not splendid.
#help
I understand that A ←s→ /B is the negation of A → B.
However, given that the meaning of 'some' is 'at least one, possibly all', does that mean that there is a possibility for A ←s→ /B to become A → /B as the negation of A → B?
I think they are using the "some are not" B to implicitly show that ALL of A is NOT B. if you say all of A --> /B then, you are saying it is never possible. However, if we had just one A that is not B then it would work for the A ←s→ /B. For EXAMple, the UC Berkeley students live in Berkeley. And then we find out that one student moves to Oakland. Then we have some students who are not living in Berkeley. If you used the A--> /B then it would reflect that none of these students live in Berekely. I'm sorry if I explained this wrong, I gave it my best shot.
also wondering
#help Can I negate it to not all Jedi use the force
didnt we just talk about how "some" could mean "all" but now thats not the case? dude
@GDatria715 I just take it as them saying it shouldn’t be the default.
In a real life situation, if I’m saying “not all” then the first assumption is “some”.
Let’s say you’re having a party and you invite 100 people. Someone asks you if every one coming to the party and you say, no not all. Most people will then follow up with: “Oh okay. Well, how many people are coming?” So it’s like the default in real life is “some” and while it COULD be “none”, the LSAT will try to trick you if you default to that.
I could be wrong tho.
@GDatria715 you’re missing the core meaning in all of this.
If we have the statement: all dogs are friendly. The negated statement (proving the statement false) is just saying this: some (from 1-100%) dogs are not friendly.
It could be all dogs aren’t friendly or only 1 dog in the universe is not friendly. We can’t infer from the original statement. The some in the negated sentence spans the entire potential cases for which you could negate the original statement.
are the sentences "its not the case that all dogs are friendly" and "some dogs are not friendly" logically equivalent?
@Luna Yes I believe so. "Its not the case that all dogs are friendly" denies that all dogs are friendly. This translates to "some dogs are not friendly".
To me it's confusing to include /(D -> F) because in algebra, you would distribute whatever is outside of the parenthesis and get /D -> /F. But in Lawgic, it really means to negate the necessary condition to create a condition that contradicts the original claim. And you can't contradict the original claim without having the non-negated sufficient condition. If you negate the sufficient condition, then you are talking about a different scenario than the one you're trying to negate. That's how I'm interpreting these lessons, let me know if I have anything wrong though
Was the F--->F to /(D-->F) turns into D <-S-> /F not taught anywhere before this???
wasnt it said earlier that "some" cannot have a contrapositive? or is negation different
@Tannercho06897 Contrapositive and negation are different!
Contrapositive is an equivalent way of expressing the relationship. We typically create a contrapositive of a normal conditional relationship (ex. cats are mammals) by flipping sufficient and necessary conditions, and negating each condition (ex. if not a mammal, then not a cat). These are two ways of expressing the same relationship.
Negation of an All statement/relationship ("it is not the case that all ...") is creating the opposite of the relationship. For example, the negation of "all cats are mammals" would be "some cats are not mammals". They express totally different relationships between the sets.
@ckilk Great point on differentiating negation and contrapositive! But I thought negation was different from the opposite?
@ckilk I am struggling with this distinction too. How do I know that the statement "all dogs are friendly" is not a conditional? My instinct was to put it into lawgic as "if dog --> friendly" and "/friendly --> /dog." Why can't I do that? Thanks!
@Hashibiro You can treat "all dogs are friendly" as "if dog --> friendly"! But, when you negate that whole relationship you want to turn it into "not all dogs are friendly" or "some dogs are not friendly".
To say "/friendly --> /dog" means "if it is not friendly, then it is not a dog" which is the same as saying "all dogs are friendly" . So you've just written "if dog --> friendly" in an equivalent way that expresses the same idea (the contrapositive). This chapter is about negating a whole Statement saying that "it is not the case that Statement is true"
@ArthurMorgan Good point! I guess this depends on the subtleties of your interpretation of the word "opposite". I just wanted to use a term other than "negate" and it made sense to me. :)
If you see the "opposite" of "left" to be "right", then "opposite" is probably not a good term to use for your personal understanding because as you said, this is not the same as negating.
If you see the "opposite" of "left" to be "not left" (which could be straight or really any other direction that is not left), then you're probably in the same frame of mind I was when I wrote my OG comment
So the difference between the contrapositive and the negation of a claim is that contrapositive reverses and negates to be logically equal to original. Negation of a claim means creating a contradictory statement.
Example : if it rains the ground is wet
R--> G
contrapositive: if the ground is not wet, it did not rain
/G-->/R
negation: it rains but the ground is not wet
R and /G
is this correct reasoning?
All pens are black
P -> B
Negated: Some pen's are not black
P <-S-> /B
To negate all relationships we are saying "It' not the case that all pens are black".
What this does not mean is all pens -> /black. THIS IS A TRAP. All this negated statement means is that "Some pens are not black"
Original: All A are B
Negated: Most A are not B ?
@PranjalChaudhary Not most, but some. We don't know what percentage of the A group that is not B. Most means more than half. It could just be one A that is not B, and some encompasses that range.
So, in this lesson we're learning how to negate a relationship, but previously we were negating conditions/logic? I'm a bit confused on how to put into words the difference between
A->B
/B->/A
and this new process that goes:
A->B
AB
If the indicator word is "all", how do you know whether to take the negation of the sufficient condition or this new negation process for "some"? Or does it boil down to what the question stem asks? Thanks in advance for any help, I'm a bit too confused to explain what exactly is confusing me...
@miadiscipio
So you're talking about two different concepts that visually look similar.
Contrapostive: Rephrasing of conditional statement that does NOT deny it.
Negation: Denying the conditional statement.
We'll use an example to flesh these two out.
Conditional Logic: A > B
Every instance of A there is B.
Contrapostive: /B > /A
Every instance of not B there is no A. Logically the exact same as the original statement.)
Negation: /(A > B)
Not every instance of A will there be B.
Negation: A <s> /B
At least one instance of A there is not B (some lower boundary is one).
How is this applicable? Off the top of my head you get some passage about how A > B but the auther disagrees with this conditional statement being true. Then you're given this question stem:
"Which of the following most strongly supported by the statements in the stimulus?"
Most instance of A there B may not appear
When B is not happening, then A would appear.
Every instance of A is not B.
There is at least once instance of A where it's not B. (correct answer)
This is a bit straight forward, and of course it's spelled out for you this way, but, it should give you a rough idea of what may appear.
Couldn't we just say "not all dogs are friendly" in order to negate "all dogs are friendly"? Is there a difference between "not all dogs are friendly" and "some dogs are not friendly"?
Yes we can write it that way as shown in the written explanation above.
The only difference I can tell is ease of understanding.
Original: D → F
Translated: All dogs are friendly.
Negated: /(D → F)
Translated: "Not all dogs are friendly."
Translated: It's not the case that all dogs are friendly.
Negated: D ←s→ /F
Translated: Some dogs are not friendly.
Trap: D → /F
Translated: All dogs are not friendly.
so is it still correct to say, "Not all dogs are friendly." ?
Yes, it's the same thing as saying "it's not the case that all dogs are friendly" which also means "some dogs are not friendly" because they are not in the intersection between the "dogs" set and the "friendly (beings)" set, therefore, they are "not friendly"