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?
#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."
In probability theory the sum of the probabilities that some event A occurs and doesn't occur would be equivalent to 1. This means that finding the probability some event A occurs, given that you know the probability it won't occur, is 1 - the probability it won't occur.
If I flipped 5 coins and asked for the probability that heads occurred at least once, I could find number of times exactly 1 coin is heads, exactly 2, exactly 3, exactly 4, and exactly 5. Which is a lot to compute. So instead, you can just consider the negation of at least once, which is none. It's much easier find the probability that heads doesn't occur at all (all tails, 1/32), and subtract that from 1. Just one way to think about it - especially useful if you have knowledge of probability.
I had to watch this a couple of times, and for me it was a great example of my intuitive thinking taking over my logical thinking. Even though it's so obviously simple when you draw the negation of "some" with circles, splitting the Venn diagram, thinking out loud to myself that "It is not true that some parrots are clever" is equivalent to saying "No parrots are clever" drove me nuts. I kept automatically thinking "well, if it is not true that some parrots are clever, maybe it's true that many/all/several parrots are clever" - always forgetting that you can't have all parrots being clever if some parrots aren't clever.
Whew!
All of which is to say - thank you for the diagrams!
"Some" refers to 1-100. To deny the existence of "some", it has to be something that is not 1-100, which means 0. Therefore, the negation of some is none.
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58 comments
Could someone explain, in the parrot example, the outcome of the negated statement was:
Parrot --> /Clever
Would it also work to say:
Clever --> /Parrot
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!
Would I be correct in saying "fewer than some is none"
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 ?
#help
Can someone explain how the distribution of the "not" symbol is working here?
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!
why do you only distribute the negation symbol to one set??? #help
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
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?
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
#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."
Why is the negated conditional statement A and /B and the some statement A → /B?
Shouldn't they both be (A → /B) in the negated form?
In probability theory the sum of the probabilities that some event A occurs and doesn't occur would be equivalent to 1. This means that finding the probability some event A occurs, given that you know the probability it won't occur, is 1 - the probability it won't occur.
If I flipped 5 coins and asked for the probability that heads occurred at least once, I could find number of times exactly 1 coin is heads, exactly 2, exactly 3, exactly 4, and exactly 5. Which is a lot to compute. So instead, you can just consider the negation of at least once, which is none. It's much easier find the probability that heads doesn't occur at all (all tails, 1/32), and subtract that from 1. Just one way to think about it - especially useful if you have knowledge of probability.
I had to watch this a couple of times, and for me it was a great example of my intuitive thinking taking over my logical thinking. Even though it's so obviously simple when you draw the negation of "some" with circles, splitting the Venn diagram, thinking out loud to myself that "It is not true that some parrots are clever" is equivalent to saying "No parrots are clever" drove me nuts. I kept automatically thinking "well, if it is not true that some parrots are clever, maybe it's true that many/all/several parrots are clever" - always forgetting that you can't have all parrots being clever if some parrots aren't clever.
Whew!
All of which is to say - thank you for the diagrams!
Could the translated negation also read C-->/P ? That's what I intuitively did because in my head I say "No parrots are clever"
What is the point of negating on the LSAT
Something that helped me understand:
"Some" refers to 1-100. To deny the existence of "some", it has to be something that is not 1-100, which means 0. Therefore, the negation of some is none.
Hope this helps :)
i'm tired of this grandpa :(