@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.
Why is the negation of all not none? ->In formal logic, the negation of a statement is defined as the weakest possible claim that contradicts the original statement. It is the "minimum requirement" to prove the original statement false.
@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
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
@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
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!!
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
But if I say that not all dogs are friendly, can we infer, or can we deny, that no dogs are friendly? It doesn't half to be the case but its not outside the realm of possibility here.
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.
@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.
@ConqueringLSAT I think it can be if you understand what all means intuitively. We're just explicitly saying 'it's not the case that all dogs are friendly' so you don't fall into the trap of thinking not all means none.
129 comments
Thank you. This makes sense.
Could it not be the case that all dogs are not friendly though?
can't we also just say that "all dogs are friendly" negated is "not all dogs are friendly"?
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.
Why is the negation of all not none? ->In formal logic, the negation of a statement is defined as the weakest possible claim that contradicts the original statement. It is the "minimum requirement" to prove the original statement false.
What would "not all dogs are not friendly mean?"
@JamesFoleno some dogs are not friendly, some dogs are not not friendly
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
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
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
I think not all is logically equivalent to some are not.
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!!
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?
But if I say that not all dogs are friendly, can we infer, or can we deny, that no dogs are friendly? It doesn't half to be the case but its not outside the realm of possibility here.
@Garrett_dom It's possible that no dogs are friendly. We can't infer that it's true, but it hasn't been ruled out.
Where would we use this idea of negating "all"? Like what question type on the lsat?
1. SOME DOGS ARE FRIENDLY
At least one dog is friendly
Not all dogs are not friendly
Negate: No dog is friendly
All dogs are not friendly.
2. ALL DOGS ARE FRIENDLY: 100% dogs->F
Negate: It’s not the case that all dogs are friendly.
Not all dogs are friendly: >100% dogs->F
Some dogs are not friendly
Arbys
@JDMurphy get this man some arbys
Do not confuse this with the creation of contrapositives which are logically equivalent to the original statement.
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.
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"
Can this be applicable to "any" and "every"?
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.
I'm confused on why it can't be "Not all A are B" instead of bringing some in it
@ConqueringLSAT I think it can be if you understand what all means intuitively. We're just explicitly saying 'it's not the case that all dogs are friendly' so you don't fall into the trap of thinking not all means none.