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
@16dnholli Thinking of this like math, you'd think that the slash would distribute, but this isn't math since we're only using arrows and symbols to represent language and short-hand logic.
/P <-s-> /C would mean "Some non-parrots are not clever". This really isn't the opposite of the original statement "Some parrots are clever".
Since "some" means anywhere from 1% to 100% of the parrots are clever, the opposite of a "some" relationship means that we have to be outside those boundaries to negate -- at 0%. So the opposite of "Some parrots are clever" is that "No parrots are clever". And if we make that statement into Lawgic it becomes P-->/C.
how is "some parrots are not clever" which was cited as an incorrect interpretation of the negated, "Some parrots ARE clever," different from "all parrots are not clever." Wouldn't "all parrots are not clever" include the "some"?
@cworth1512 "Some parrots are not clever" doesn't contradict "Some parrots are clever". You're right that "All parrots are not clever" implies that "some parrots are not clever," but the issue is the negation needs to contradict the original statement. The negation should be an expression of the minimum that's required to make the original statement logically impossible.
Is it correct to view your transition from "no parrots are clever" to "all parrots are not clever" as an application of the group four negate negate necessary? My mind just processes it quicker that way; for the LSAT, the less memory I have to use, the better. So I can roll with the idea that "no parrots are clever" works out to P--->/C due to Group 4 Negate Necessary that would be just swell.
I completely understand that the negated version of "some parrots are clever" is both "no parrots are clever" and all parrots are not clever". However, I do not understand why P <--S--> C ONLY translates to P-->/C and why it does not ALSO translate to /P --> C. I would think that P-->/C would be "all parrots are not clever" and that /P--> C would be "No parrots are clever"? Am i thinking of this the wrong way? Or was it supposed to be implied in the video that the negative (/) can "flip" around the arrow to either side?
@BaileyB I think this might be because "No" is a Group 4 Indicator, meaning it's negate necessary. So the negated part would go to the necessary part of the claim. So if it's no parrots are clever, then it would be P --> / C. The contrapositive of this would be C --> /P. Therefore, my thinking is that /P--> C would be confusing sufficiency for necessity
@brendan.curran.paul I'm not sure what you mean by negating "some" in the positive sense. It looks to me like that example involves interpreting "Some" as if it means "Less than all". Under this interpretation, the negation of "less than all" becomes "all."
But the problem is "some" doesn't have to imply "less than all." It just means "at least one." So negating "some" must mean 0 (your first example).
Note that informally people often use "some" to mean "some, but not all". But "some" just means "at least one" (without expressing an opinion about whether the quantity could include all).
@Kevin_Lin Thank you for this clarification. However could I trouble you for some additional insights into this, as your comment just sparked something in my brain as to whether it could be possible to understand the above to be in a parallel relationship with negating the "All" quantifier, namely:
[Negating "Some"]
1) Initial: Some A are B (A <-s-> B)
2) Negates to: No A are B (A -> /B)
[Negating "All"]
3) Initial: All A are B (A -> B)
4) Negates to: Some A are not B (A <-s-> /B)
But notice that the 1) and 4) above, don't they amount to saying the same thing? Namely, saying "some A are B" effectively the same thing as "some A are not B" (A <-s-> B = A <-s-> /B?)
IF it is the case that the above statements 1) and 4) mean the same thing, shouldn't their contrapositives 2) and 3) also effectively mean the same thing? Ah but here I realized I walked into a contradiction, as there's no way "No A are B" would mean the same as "All A are B"...!
Thanks for indulging me as I thought aloud here--but I guess my qualm with 1) and 4) above still stands, that whether defining "Some" to mean "at least one" rather than "less than all" would be considered more a matter of linguistic convention than it is a matter of strict logic.
The motive for asking this question also stems partly from the fact that I do not come from an English-speaking country, and could not help comparing the meaning of "some" in English to the meaning of "some" in certain other languages.
@brendan.curran.paul Usually, in a real life context, the only reason you'd say "some A are B" is because you're in a situation in which people recognize that some/most A are NOT B. So you're trying to emphasize that some of them are.
And in a real life context, often the only reason you'd say "some A are NOT B" is because you're in a situation in which people recognize that some/most A are B, and you're trying to emphasize that this isn't true for all As.
But when you examine the language itself -- "some A are B" -- it really does just mean "at least one A is B" without expressing any opinion about whether any As are NOT B. And "some A are NOT B" really does just mean "at least one A is NOT B" without expressing any opinion about whether any As are B.
It's a good idea to just translate "some" to "at least one."
"Some tests are difficult" = At least one test is difficult
Are there any tests that aren't difficult? We don't know based on that statement.
"Some people are friendly" = At least one person is friendly
Are there any people that aren't friendly? We don't know based on that statement.
"Some police officers are not corrupt." = At least one police officer is not corrupt.
Are there any police officers that are corrupt? We don't know based on that statement.
"No vegetables taste good." = If vegetable --> NOT taste good
"No dogs can fly." = If dogs --> NOT fly
"No" at the beginning of a statement can be confusing; you might think it applies to the beginning of the sentence. That's why you think "No A are B" starts with "If NOT A..." But that's not the right understanding.
@Gabbienixon Nevermind! found my answer from instructor Kevin below:
No, it's not.
If A, then Not B.
The contrapositive is:
If B, then Not A.
In other words, A and B are two entirely separate categories. If you're in one, you're not in the other.
That's what "No A is B" means.
"No A are B" does NOT mean "/A --> B". "/A --> B" means everything that's not an A must be B. That's different from saying if something is an A, then it's not a B.
we are denying the intersection of the relationship in its entirety. Because few= at least 1 we must go with the definitive no claim to establish that no vegans are in fact kind
I understand that we are trying to deny the "some" intersection, but why can't negating "some A are B" lead to "few A are B" if it is smaller on the hierarchy?
I don't understand how and why to use the -s-> and the --> in relation with each other. should we stick to lawgic without quantifies unless the question introduces a quantifier?
if the words "no" or "none" or the phrase "it's not the case that" etc., pop up, then it falls under the rule of negating either condition and making it the necessary condition. That's why some (at least 1) A are B negated is some (at least 1) A are not B, and the contrapositive would be: B --> /A
if we apply the example from the students can read with 20 students in the class and "some" indicates that there must be true that at least one for the lower boundary, is the negating addressing what must be false then that 0 can read?
In other words, A and B are two entirely separate categories. If you're in one, you're not in the other.
That's what "No A is B" means.
"No A are B" does NOT mean "/A --> B". "/A --> B" means everything that's not an A must be B. That's different from saying if something is an A, then it's not a B.
#feedback, can I accurately negate "some" with "all/no" without concerning myself with the preface is it not the case"? Essentially whenever/wherever I am negating "some" just treat it as "all/no."
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69 comments
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
I think I'm confusing the difference between the contrapositive and negating...
I don't understand how:
/(P <-s-> C) does not equal /P <-s->/C
Why does the slash only distribute to C and how do we know to only distribute it to C?
@16dnholli Thinking of this like math, you'd think that the slash would distribute, but this isn't math since we're only using arrows and symbols to represent language and short-hand logic.
/P <-s-> /C would mean "Some non-parrots are not clever". This really isn't the opposite of the original statement "Some parrots are clever".
Since "some" means anywhere from 1% to 100% of the parrots are clever, the opposite of a "some" relationship means that we have to be outside those boundaries to negate -- at 0%. So the opposite of "Some parrots are clever" is that "No parrots are clever". And if we make that statement into Lawgic it becomes P-->/C.
how is "some parrots are not clever" which was cited as an incorrect interpretation of the negated, "Some parrots ARE clever," different from "all parrots are not clever." Wouldn't "all parrots are not clever" include the "some"?
@cworth1512 "Some parrots are not clever" doesn't contradict "Some parrots are clever". You're right that "All parrots are not clever" implies that "some parrots are not clever," but the issue is the negation needs to contradict the original statement. The negation should be an expression of the minimum that's required to make the original statement logically impossible.
Just want to randomly pop in and wish everyone luck in their studying! I took a break from it, but I'm back!
Is it correct to view your transition from "no parrots are clever" to "all parrots are not clever" as an application of the group four negate negate necessary? My mind just processes it quicker that way; for the LSAT, the less memory I have to use, the better. So I can roll with the idea that "no parrots are clever" works out to P--->/C due to Group 4 Negate Necessary that would be just swell.
honestly, this doesn't need to be overthought. Just trust your intuition...
I completely understand that the negated version of "some parrots are clever" is both "no parrots are clever" and all parrots are not clever". However, I do not understand why P <--S--> C ONLY translates to P-->/C and why it does not ALSO translate to /P --> C. I would think that P-->/C would be "all parrots are not clever" and that /P--> C would be "No parrots are clever"? Am i thinking of this the wrong way? Or was it supposed to be implied in the video that the negative (/) can "flip" around the arrow to either side?
@BaileyB I think this might be because "No" is a Group 4 Indicator, meaning it's negate necessary. So the negated part would go to the necessary part of the claim. So if it's no parrots are clever, then it would be P --> / C. The contrapositive of this would be C --> /P. Therefore, my thinking is that /P--> C would be confusing sufficiency for necessity
Could someone explain, in the parrot example, the outcome of the negated statement was:
Parrot --> /Clever
Would it also work to say:
Clever --> /Parrot
@SamI_02 I do believe that is the contrapositive, so yes it would work
Question:
If what we are doing is denying the "some" relationship, couldn't the negation work both in the negative and in the positive senses?
Namely:
['Negative' negation]
Initial: Some parrots are clever.
1st step: It's not the case that some parrots are clever.
Final: No parrots are clever.
['Positive' negation]
Initial: Some parrots are clever.
1st step: It's not the case that some parrots are clever.
Final: All parrots are clever.
If any error(s) in logic were made above, would appreciate corrections and explanations. Many thanks!
@brendan.curran.paul I'm not sure what you mean by negating "some" in the positive sense. It looks to me like that example involves interpreting "Some" as if it means "Less than all". Under this interpretation, the negation of "less than all" becomes "all."
But the problem is "some" doesn't have to imply "less than all." It just means "at least one." So negating "some" must mean 0 (your first example).
Note that informally people often use "some" to mean "some, but not all". But "some" just means "at least one" (without expressing an opinion about whether the quantity could include all).
@Kevin_Lin Thank you for this clarification. However could I trouble you for some additional insights into this, as your comment just sparked something in my brain as to whether it could be possible to understand the above to be in a parallel relationship with negating the "All" quantifier, namely:
[Negating "Some"]
1) Initial: Some A are B (A <-s-> B)
2) Negates to: No A are B (A -> /B)
[Negating "All"]
3) Initial: All A are B (A -> B)
4) Negates to: Some A are not B (A <-s-> /B)
But notice that the 1) and 4) above, don't they amount to saying the same thing? Namely, saying "some A are B" effectively the same thing as "some A are not B" (A <-s-> B = A <-s-> /B?)
IF it is the case that the above statements 1) and 4) mean the same thing, shouldn't their contrapositives 2) and 3) also effectively mean the same thing? Ah but here I realized I walked into a contradiction, as there's no way "No A are B" would mean the same as "All A are B"...!
Thanks for indulging me as I thought aloud here--but I guess my qualm with 1) and 4) above still stands, that whether defining "Some" to mean "at least one" rather than "less than all" would be considered more a matter of linguistic convention than it is a matter of strict logic.
The motive for asking this question also stems partly from the fact that I do not come from an English-speaking country, and could not help comparing the meaning of "some" in English to the meaning of "some" in certain other languages.
Hoping to hear back - Many thanks!
@brendan.curran.paul Usually, in a real life context, the only reason you'd say "some A are B" is because you're in a situation in which people recognize that some/most A are NOT B. So you're trying to emphasize that some of them are.
And in a real life context, often the only reason you'd say "some A are NOT B" is because you're in a situation in which people recognize that some/most A are B, and you're trying to emphasize that this isn't true for all As.
But when you examine the language itself -- "some A are B" -- it really does just mean "at least one A is B" without expressing any opinion about whether any As are NOT B. And "some A are NOT B" really does just mean "at least one A is NOT B" without expressing any opinion about whether any As are B.
It's a good idea to just translate "some" to "at least one."
"Some tests are difficult" = At least one test is difficult
Are there any tests that aren't difficult? We don't know based on that statement.
"Some people are friendly" = At least one person is friendly
Are there any people that aren't friendly? We don't know based on that statement.
"Some police officers are not corrupt." = At least one police officer is not corrupt.
Are there any police officers that are corrupt? We don't know based on that statement.
@Kevin_Lin Thank you for clearing this up for me! Appreciate it a lot :)
Would I be correct in saying "fewer than some is none"
@CodyLevant That makes sense. Some means at least one, so if we want to express fewer than at least one, we must mean zero.
Following this logic:
Original: Some A are B
Negated: No A are B
Original: A ←s→ B
Negated: A → /B
Why isn't the last part no /A→ B, because the negated above reads No A are B ?
@nelsonmartins "No A are B" = If A, then NOT B
"No vegetables taste good." = If vegetable --> NOT taste good
"No dogs can fly." = If dogs --> NOT fly
"No" at the beginning of a statement can be confusing; you might think it applies to the beginning of the sentence. That's why you think "No A are B" starts with "If NOT A..." But that's not the right understanding.
#help
Can someone explain how the distribution of the "not" symbol is working here?
@bappel
Example: Some A are B.
Lawgic: A <-s-> B.
Negate: No A are B or All A are not B, which are equitant to if A, the not B.
Lawgic: /(A <-s-> B) which is equivalent to A --> /B.
Could we distribute the negation to A instead of B as to say /A > B or does the negation have to go on the B set (A >/B)
if we can say No parrots are clever would that not follow as /P>C
or does it have to negate the C (clever) P>/C ? confused why we the negation is No A are B with the Negation slash on the B
help!
@Gabbienixon Nevermind! found my answer from instructor Kevin below:
No, it's not.
If A, then Not B.
The contrapositive is:
If B, then Not A.
In other words, A and B are two entirely separate categories. If you're in one, you're not in the other.
That's what "No A is B" means.
"No A are B" does NOT mean "/A --> B". "/A --> B" means everything that's not an A must be B. That's different from saying if something is an A, then it's not a B.
why do you only distribute the negation symbol to one set??? #help
@CeciliaBurton1
Some cats are furry, C <-S-> F.
Distributing "/" to both, /C -> /B which will be something like "Not/non cats are not furry" or "if not a cat, then not furry".
That is very different from negation.
Negate: C ->/F which is "All cats are not furry" or "If cat, then not furry".
so for example some vegans are kind
Negated: No vegans are kind
we are denying the intersection of the relationship in its entirety. Because few= at least 1 we must go with the definitive no claim to establish that no vegans are in fact kind
I understand that we are trying to deny the "some" intersection, but why can't negating "some A are B" lead to "few A are B" if it is smaller on the hierarchy?
all->most->many->some->few
@ktacklesthelsat some and both imply some intersection, so the negation of that is no intersection at all
I don't understand how and why to use the -s-> and the --> in relation with each other. should we stick to lawgic without quantifies unless the question introduces a quantifier?
if the words "no" or "none" or the phrase "it's not the case that" etc., pop up, then it falls under the rule of negating either condition and making it the necessary condition. That's why some (at least 1) A are B negated is some (at least 1) A are not B, and the contrapositive would be: B --> /A
if we apply the example from the students can read with 20 students in the class and "some" indicates that there must be true that at least one for the lower boundary, is the negating addressing what must be false then that 0 can read?
What is the importance of this? I do not get when and how I would use this?
/(A ‑m→ B)
or
A ←s→ /B
Is this correct?
Would you negate most statements like all statements?
/(A ‑m→ B)
or
A ←s→ /B
Is this correct?
is anyone getting confused about how these transitions to lawgic are working
Is A --> /B the same thing as /A --> B?
It just makes more sense to me to translate "No A are B" to /A --> B rather than A --> /B
No, it's not.
If A, then Not B.
The contrapositive is:
If B, then Not A.
In other words, A and B are two entirely separate categories. If you're in one, you're not in the other.
That's what "No A is B" means.
"No A are B" does NOT mean "/A --> B". "/A --> B" means everything that's not an A must be B. That's different from saying if something is an A, then it's not a B.
#feedback, can I accurately negate "some" with "all/no" without concerning myself with the preface is it not the case"? Essentially whenever/wherever I am negating "some" just treat it as "all/no."