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).
there needs to be more application to real lsat questions for these logic lessons because just saying if A then B does not help to visualize what it actually means and how it can be applied when doing questions
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.
@AnyahJoseph815 BRO ME TOOOOOOOOOO i feel like he shouldve made that distinction especially after moving on from conditional statements like i was breaking my head
#feedback Most of these logic lessons should have a real-case LSAT question in each lesson after the explanation to really seal the information. With the idea of constant A B C and Ds it becomes repetitive and extremely hard to concentrate
I believe this lesson is introducing the idea that not all conditional claims have to be true.
Example: I can make the claim that to go on Love Island, you have to be attractive.
The contrapositive is: If you are not attractive, you cannot go on Love Island.
Meanwhile, the negation is trying to say, "Wait. That's just not true."
The negation would be: It's not the case that if you are not attractive, you cannot go on Love Island. You can go on Love Island and not be attractive. Love Island does not require you to be attractive.
This part of the lesson should be moved earlier in the conditional logic curriculum, before students learn the contrapositive, to avoid confusion. Many people are mixing up negation with the contrapositive.
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)?
@jaydenca I'm thinking about it this way: I need to know how to take the contrapositive so that I can recognize an alternative version of a claim. So let's say a conclusion in a stimulus is "If it's a dog, then it's a mammal" and the question is to identify what is the conclusion. Most likely they are going to rephrase it to disguise the conclusion using a logical trick, and this is where it's useful to employ the contrapositive. Why? Because it preserves the logical meaning of the conclusion and is just rephrasing it. So I could be faced with the following choice:
A. If it is not a mammal, then it is not a dog.
And I know that that's my answer bc it contraposes the statement: "if it's a dog, then it's a mammal."
But then when do you use the negation? One example is on a question where they ask "which statement, if true, weakens the argument,"you can start by finding a negation to the conditional claim so you can deny the conditional relationship and therefore weaken the argument. Remember, a negation is all about destroying the relationship and a contrapositive is about rephrasing and preserving the validity of a logical relationship.
So let's turn the Jedi example into a question stimulus: To be a Jedi, one must be able to use the Force. After all, the Force is the only known source of power for Jedis in the galaxy.
So if I want to weaken this argument and its conclusion, I need a statement that helps me to achieve its negation, and a possible valid negation is: "Being a Jedi does not require being able to use the Force."
Then I take that negation and I look at my answer choices and find the one that, if true, destroys that conditional relationship by helping me fulfill the negation I came up with. So lets say an answer choice they give me is the following:
D. Instead of the Force, Anakin, a Jedi, has discovered and harnessed the power of the Blob, a new source of power in the galaxy.
This is your correct answer. Why? Because if it's true, it supports the statement (our negation) "Being a Jedi does not require being able to use the Force." Now that Anakin has harnessed the Blob, it's not required for him to use the Force. Boom, conditional relationship negated and destroyed.
TL;DR--finding the negation helps you use it as a metric for questions where you are asked to weaken the argument, because you need to weaken the logical relationship of the conditional. You take the negation of the claim and hold it up to your answer choices and ask "does this answer choice give me the negation?"
A contrapositive helps you rephrase and recognize your claim in other answer choices.
I hope this helps! And if I got something wrong, someone please correct me, I don't want to confuse people.
@BreanaNunez I am confused why wouldn't we negate this as like how we usually do. /sick --> / sleep? How can you tell the difference on which way to make the contrapositive.
@anulirz Hey! so from my understanding... if I were to read out loud /sick -> /sleep it would translate to "if the toddler is not sick then they will not sleep all day", which is completely different from the original statement: "if a toddler is sick then they will want to sleep all day". In this, we are trying to DENY the statement that just because they're sick they will want to sleep all day. How do we deny that? I personally say out loud like okay well that doesn't have to be true the toddler CAN still be sick and NOT want to sleep all day. Then translating to sick AND /sleep. Does that help at all?
It would've been nice to get an explanation on the difference between a contrapositive statement and a negated statement because I was wondering why we can't just say:
"To be a Jedi, one must be able to use the Force."
J → F
"If you don't know how to use the Force, you are not a Jedi"
/F → /J
but I realize that we just need to negate the sufficient condition for “All” conditional statements, correct?
"To be a Jedi, one must be able to use the Force." Translates to "All Jedis must be able to use the Force."
“It's not the case that all Jedis must be able to use the Force”
@timwes21 Yeah this is a pretty big oversight. Essentially, A->B is equivalent to /A or B (also called Conditional disintegration), so When you negate (/A or B) your get (A and /B)
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")
I watched this lesson thinking it was taking the contrapositive of the claim cause of the use of negation. But then I realized they were two different things...
if we understand these already, can we just skip over them? I feel there's no purpose in adding complexity or more context to something we can easily understand on it's own.
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?
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
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?
181 comments
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).
@natcat You made a great comment. I felt I understood the lesson, but I did not make this distinction.
@natcat When do you know whether to use the contrapositive technique or the negation technique?
@natcat very well put. This should've been one of the first things they told us in this lesson set on negation.
@iwillcrushthelsat yes still wondering about this question.
@MPFerrari right!? :(
there needs to be more application to real lsat questions for these logic lessons because just saying if A then B does not help to visualize what it actually means and how it can be applied when doing questions
the trap is definitely trapping
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.
I think this whole time I have been using contrapositive and negation as equivalents when they are not.
@AnyahJoseph815 BRO ME TOOOOOOOOOO i feel like he shouldve made that distinction especially after moving on from conditional statements like i was breaking my head
#feedback Most of these logic lessons should have a real-case LSAT question in each lesson after the explanation to really seal the information. With the idea of constant A B C and Ds it becomes repetitive and extremely hard to concentrate
I believe this lesson is introducing the idea that not all conditional claims have to be true.
Example: I can make the claim that to go on Love Island, you have to be attractive.
The contrapositive is: If you are not attractive, you cannot go on Love Island.
Meanwhile, the negation is trying to say, "Wait. That's just not true."
The negation would be: It's not the case that if you are not attractive, you cannot go on Love Island. You can go on Love Island and not be attractive. Love Island does not require you to be attractive.
@DevanshiPatel thanks, now i can go to love island
@DevanshiPatel makes sm more sense lol thanks!!!!
@DevanshiPatel These are the types of examples they should be using
im never viewing star wars the same after this curriculum.
Denying/negating the relationship means the sufficient condition can exist without the necessary condition
@VanillaCat ooo i like this thank you
This part of the lesson should be moved earlier in the conditional logic curriculum, before students learn the contrapositive, to avoid confusion. Many people are mixing up negation with the contrapositive.
Months later still coming back to review this
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)?
@rugin.geramifard It could be based on the question stem? Possibly when you encounter a stem that indicates something of its negation/contradiction.
@rugin.geramifard I'm guessing contrapositives apply to MBT questions or similar stems
How would we know when to negate a relationship vs taking the contrapositive? I'm slightly confused about this.
@jaydenca I'm thinking about it this way: I need to know how to take the contrapositive so that I can recognize an alternative version of a claim. So let's say a conclusion in a stimulus is "If it's a dog, then it's a mammal" and the question is to identify what is the conclusion. Most likely they are going to rephrase it to disguise the conclusion using a logical trick, and this is where it's useful to employ the contrapositive. Why? Because it preserves the logical meaning of the conclusion and is just rephrasing it. So I could be faced with the following choice:
A. If it is not a mammal, then it is not a dog.
And I know that that's my answer bc it contraposes the statement: "if it's a dog, then it's a mammal."
But then when do you use the negation? One example is on a question where they ask "which statement, if true, weakens the argument," you can start by finding a negation to the conditional claim so you can deny the conditional relationship and therefore weaken the argument. Remember, a negation is all about destroying the relationship and a contrapositive is about rephrasing and preserving the validity of a logical relationship.
So let's turn the Jedi example into a question stimulus: To be a Jedi, one must be able to use the Force. After all, the Force is the only known source of power for Jedis in the galaxy.
So if I want to weaken this argument and its conclusion, I need a statement that helps me to achieve its negation, and a possible valid negation is: "Being a Jedi does not require being able to use the Force."
Then I take that negation and I look at my answer choices and find the one that, if true, destroys that conditional relationship by helping me fulfill the negation I came up with. So lets say an answer choice they give me is the following:
D. Instead of the Force, Anakin, a Jedi, has discovered and harnessed the power of the Blob, a new source of power in the galaxy.
This is your correct answer. Why? Because if it's true, it supports the statement (our negation) "Being a Jedi does not require being able to use the Force." Now that Anakin has harnessed the Blob, it's not required for him to use the Force. Boom, conditional relationship negated and destroyed.
TL;DR--finding the negation helps you use it as a metric for questions where you are asked to weaken the argument, because you need to weaken the logical relationship of the conditional. You take the negation of the claim and hold it up to your answer choices and ask "does this answer choice give me the negation?"
A contrapositive helps you rephrase and recognize your claim in other answer choices.
I hope this helps! And if I got something wrong, someone please correct me, I don't want to confuse people.
@DollyPartonStan This was a phenomenal explanation. Precisely what I needed to read to understand.
@DollyPartonStan this really helped me understand, thank you!!
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
@BreanaNunez I am confused why wouldn't we negate this as like how we usually do. /sick --> / sleep? How can you tell the difference on which way to make the contrapositive.
@anulirz Hey! so from my understanding... if I were to read out loud /sick -> /sleep it would translate to "if the toddler is not sick then they will not sleep all day", which is completely different from the original statement: "if a toddler is sick then they will want to sleep all day". In this, we are trying to DENY the statement that just because they're sick they will want to sleep all day. How do we deny that? I personally say out loud like okay well that doesn't have to be true the toddler CAN still be sick and NOT want to sleep all day. Then translating to sick AND /sleep. Does that help at all?
It would've been nice to get an explanation on the difference between a contrapositive statement and a negated statement because I was wondering why we can't just say:
"To be a Jedi, one must be able to use the Force."
J → F
"If you don't know how to use the Force, you are not a Jedi"
/F → /J
but I realize that we just need to negate the sufficient condition for “All” conditional statements, correct?
"To be a Jedi, one must be able to use the Force." Translates to "All Jedis must be able to use the Force."
“It's not the case that all Jedis must be able to use the Force”
/J → F
This was a helpful way to look at it, thanks!
How is an arrow negated to an “and” this was not covered before
@timwes21 Yeah this is a pretty big oversight. Essentially, A->B is equivalent to /A or B (also called Conditional disintegration), so When you negate (/A or B) your get (A and /B)
does "some A are not B" or "A <-s-> /B" work here as well? (Some Jedis do not have to use the force..?}
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")
I watched this lesson thinking it was taking the contrapositive of the claim cause of the use of negation. But then I realized they were two different things...
SAME! I fell into my own trap lol
sameee I was like what is going on right now
if we understand these already, can we just skip over them? I feel there's no purpose in adding complexity or more context to something we can easily understand on it's own.
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?
@ConqueringLSAT
Contrapositive:
If cat, then mammal
C->M
/M->/C
If not mammal, then not cat
This is the exact same sentence as: If cat, then mammal. Contrapositive is another way of saying the same things but with nots & nones.
Negation:
If cat, then not mammal
You destroy the subset superset relationship by taking out the subset out of the superset i.e. take out the cat from being a mammal.
Original statement: In order for it to be a cat, it must be a mammal.
Negated statement: In order for it to be a cat, it does not require to be a mammal. It is a cat and not a mammal.
C and /M
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
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?
Possibly used in weakening questions?
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.