Contrapositive: Creates equivalent statement. Compared to the original it only provides support, so this helps to make valid inferences from the original conditions.
Must be true question example: To qualify for scholarship, students must have a GPA above 3.5. Bob does not have a GPA above 3.5. (Qualify -> GPA > 3.5)
To know what must be true you need a contrapositive since it provides support to what is known. (/GPA > 3.5 -> /Qualify)
Negation: This purposefully contradicts the original statement. You need this to show what would make the original statement false.
We aren't there yet but this is useful in later lessons like Necessary assumptions to try and destroy an argument.
Changing poopy diapers on time makes one a good parent.
So if change then good parent. change-> good parent.
To negate this or to deny the relationship we can say it is possible to change poopy diapers on time and not be a good parent - change and /good parent. This is different from the contrapositive form, because the contrapositive is still logically equivalent. Negation disrupts the relationship between two conditions. Its not the case that changing poopy diapers makes one a good parent. This means you can be in the sufficient condition without being in the necessary condition which if you think about is completely different from the rule I laid out in my first sentence.
On the LSAT, how would we know when to negate the conclusion (/F -> /Jedi) and how do we know when to negate the whole claim like it does in this lesson?
For those confusing negation with the contrapositive:
the contrapositive is when we negate the necessary condition, which in turn negates the sufficient condition. (A-->B turns into /B-->/A) The contrapositive also allows us to understand logically equivalent claims.
When we negate "a claim about a relationship" we are not negating the necessary condition but rather the claim itself. For example, a biologist may say if cat then mammal, (C-->M) but a science skeptic may negate that and say it is not the case that if cat then mammal (C and /M).
When you attempt to negate a claim about a relationship, in this instance, a conditional relationship, you are trying deny that relationship. Same error is present in the same section of the previous lesson on "all" relationships.
I understand the difference between Negating conditional statements and taking the Contrapositive but in a question how would I know which method to use if they use the same indicator words (e.g. If-then)?
Could it also be framed as if J then F and negated as if /J and F meaning one does not need to be a Jedi to use the force? or is this wrong to negate the sufficient condition? I believe this may not work because writing /A and B could suggest not A and not B.
#feedback, with conditional the statements can I accurately negate only the " necessary condition" and not have to bother about the sufficient condition, all the time?
Why is this different from negating "all" claims in the previous section? I thought "all" was an indicator of a sufficient condition, so "All A are B" = A --> B, which is the same as "If A then B"
(i.e. "All cats are mammals" is the same as "If one is a cat, then they are a mammal")
#feedback From my understanding, negating a conditional statement (whether all, some, many, most) means that there has been at leastttt one exception where the rule (ex: If A then B) doesn't hold as opposed to negating all (or some, or most, or many, etc) to none, right?
Okay I get it now a negation is basically saying not that. so dogs are friendly the negation would be the dogs are not friendly which means that the negation is the false statement right but how is that relevant
Does anyone know a way to visually represent this with circles that would represent sets? Similar to what he did in the previous lesson about negating all?
So I understand that here we are negating the relationship - but when do we know whether to negate the relationship or if its just a contrapositive conditional or necessary statement such as: where A–> B turns into /B–>/A? And I remember a lesson earlier saying don't apply real world common knowledge to come to an answer - instead use what we have and are being told. makes sense, but for here it says to be a Jedi one must be able to use the force. So why are we negating the relationship and when will we need to?
Ok so I understand how this is different from the other thing we learned where A--> B turns into /B-->/A, but how does this compute for my notes? Like in which cases do we use both of these? Why would I be doing a negation like in this video?
I feel like nobody is going to understand this but I just figured out that J.Y. sounds so similar to Martin from Slushynoobz. Maybe I am crazy...
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118 comments
So I think for contrapositive and negation
Contrapositive: Creates equivalent statement. Compared to the original it only provides support, so this helps to make valid inferences from the original conditions.
Must be true question example: To qualify for scholarship, students must have a GPA above 3.5. Bob does not have a GPA above 3.5. (Qualify -> GPA > 3.5)
To know what must be true you need a contrapositive since it provides support to what is known. (/GPA > 3.5 -> /Qualify)
Negation: This purposefully contradicts the original statement. You need this to show what would make the original statement false.
We aren't there yet but this is useful in later lessons like Necessary assumptions to try and destroy an argument.
Denying/negating the relationship means the sufficient condition can exist without the necessary condition
if a toddler is sick then they will want to sleep all day
sick -> sleep
a toddler can be sick and not want to sleep all day
sick and /sleep
Changing poopy diapers on time makes one a good parent.
So if change then good parent. change-> good parent.
To negate this or to deny the relationship we can say it is possible to change poopy diapers on time and not be a good parent - change and /good parent. This is different from the contrapositive form, because the contrapositive is still logically equivalent. Negation disrupts the relationship between two conditions. Its not the case that changing poopy diapers makes one a good parent. This means you can be in the sufficient condition without being in the necessary condition which if you think about is completely different from the rule I laid out in my first sentence.
On the LSAT, how would we know when to negate the conclusion (/F -> /Jedi) and how do we know when to negate the whole claim like it does in this lesson?
Where do we learn about the concepts behind conditional vs set differences?
it is so messed up, i am still very confused with negating the conditional r/s.
For those confusing negation with the contrapositive:
the contrapositive is when we negate the necessary condition, which in turn negates the sufficient condition. (A-->B turns into /B-->/A) The contrapositive also allows us to understand logically equivalent claims.
When we negate "a claim about a relationship" we are not negating the necessary condition but rather the claim itself. For example, a biologist may say if cat then mammal, (C-->M) but a science skeptic may negate that and say it is not the case that if cat then mammal (C and /M).
Months later still coming back to review this
Found a typo under the "Let's Review"
When you attempt to negate a claim about a relationship, in this instance, a conditional relationship, you are trying deny that relationship. Same error is present in the same section of the previous lesson on "all" relationships.
#feedback
I understand the difference between Negating conditional statements and taking the Contrapositive but in a question how would I know which method to use if they use the same indicator words (e.g. If-then)?
Does the negation use a similar principle to simplify embedded conditionals?
Could you also negate this example to J ←s→ /F?
Could it also be framed as if J then F and negated as if /J and F meaning one does not need to be a Jedi to use the force? or is this wrong to negate the sufficient condition? I believe this may not work because writing /A and B could suggest not A and not B.
#feedback, with conditional the statements can I accurately negate only the " necessary condition" and not have to bother about the sufficient condition, all the time?
Why is this different from negating "all" claims in the previous section? I thought "all" was an indicator of a sufficient condition, so "All A are B" = A --> B, which is the same as "If A then B"
(i.e. "All cats are mammals" is the same as "If one is a cat, then they are a mammal")
#feedback From my understanding, negating a conditional statement (whether all, some, many, most) means that there has been at leastttt one exception where the rule (ex: If A then B) doesn't hold as opposed to negating all (or some, or most, or many, etc) to none, right?
Okay I get it now a negation is basically saying not that. so dogs are friendly the negation would be the dogs are not friendly which means that the negation is the false statement right but how is that relevant
So basically, NC doesn't follow from SC???
Does anyone know a way to visually represent this with circles that would represent sets? Similar to what he did in the previous lesson about negating all?
So I understand that here we are negating the relationship - but when do we know whether to negate the relationship or if its just a contrapositive conditional or necessary statement such as: where A–> B turns into /B–>/A? And I remember a lesson earlier saying don't apply real world common knowledge to come to an answer - instead use what we have and are being told. makes sense, but for here it says to be a Jedi one must be able to use the force. So why are we negating the relationship and when will we need to?
I understand this well, but what types of situations am I gonna be needing to negate conditional statements?
Ok so I understand how this is different from the other thing we learned where A--> B turns into /B-->/A, but how does this compute for my notes? Like in which cases do we use both of these? Why would I be doing a negation like in this video?
This is unfortunately not naturally intuitive for me, are there any exercises on this?
I feel like nobody is going to understand this but I just figured out that J.Y. sounds so similar to Martin from Slushynoobz. Maybe I am crazy...