@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
@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)
can someone explain how this type of negation is not a mistaken negation? How come when we're originally taught about contrapositives, we flip and negate, and for these relationships that's now incorrect?
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
@mattiesas the negation of the whole relationship!
Just like how /A meant the negation of a single condition, the parenthesis show that the negation in /(A->B) applies to the whole relationship rather than just one condition.
@CarlosHernandez03 I'm not entirely certain that that is correct, as our goal in this negation is to deny the conditional relationship; that is, we're trying to say, "We can be A without being B." I believe your statement is saying, "You don't have to be A in order to be B."
The statement, "It is not necessary to be a Jedi to use the force," does not deny the conditional relationship as it is saying, "It is not necessary to be a Jedi to use the force, but you can still be a Jedi and use the force." Therefore, it is not outright denying this conditional relationship, as we're aiming for in negation.
The phrase, "It's not the case that to be a Jedi, one must be able to use the Force," does deny this conditional relationship because it's outright shutting down the idea that there's any causation between Jediship and Force use. "It is not necessary to be a Jedi to use the force," is instead drawing a line in the sand amongst Force users while not denying this causation. Negation is aiming to deny this causation; it's aiming to deny this conditional relationship.
I hope this makes even a lick of sense; logic is incredibly hard to express in English, and I sincerely hope this doesn't come across condescending or overly-corrective in any way! Please give any feedback or thoughts you have!! Have a wonderful day and good luck on your studies!!
I can't seem to understand the difference between negating "all" statements and negating conditional statements. Isn't All A are B (A->B) logically equivalent to If A then B (A-> B)?
@KhushyMandania I was a bit confused by as well as the Lawgic translations are the same but the main difference is the difference in relation it gives between two concepts.
You can see the differences in the negations of each. All A are B is simply stating that relation, for example "All games are fun" so we see with the negation when we deny that relationship we are stating that "it isn't the case that all games are fun" or "Some A are not B" so "Some games are not fun"
Now the difference in a conditional statements is the relationship between the two concepts is different, we are not saying that "All of A is B." We are instead saying "If A happens then B."
Therefore when we deny that relationship in the negation we see the differences there as well. Stating the A is independent of be or "A can occur and B not occur."
"If I find a game is fun then I will play it with my friends"
negation
"One can find a game fun and not play it with friends"
@KhushyMandania The difference is just about whether you are negating the conditional relationship (stating that it is not the case that A is sufficient for B) or negating the "all" statement (stating that it is not the case that ALL members of set A belong to set B). If we take the example of sentence "All dogs are cute" to illustrate this point, if we want to negate the conditional relationship in this sentence, that is to state that it's not sufficient to be a dog in order to be a cute being, we therefore write in Lawgic that we have D conjunction ~C (D and ~C) . It's like saying: "Hey, here's a set in which I have a dog, and look, it's not cute.) Alternatively, if we want to negate the quantifier ALL, meaning that we want to state that NOT ALL dogs are cute, we are therefore saying that some dogs are not cute, which we express in Lawgic by writing D < -- s -- > ~C. So, for all practical purposes, whether we are going to use one kind of negation or the other depends purely on what instructions are we given in English.
@brydon125 Hey ! Could you specify what you mean here? Are you saying that /(A->B) should be /A and B, as opposed to A and /B? I was also a bit confused as to how we're distributing out the contrapositive, but I feel like the statement is correct whichever way, as long as they don't go together, since that's what we're trying to demonstrate.
@businessgoose I came by to see if anyone else had said what @brydon125 did. I think @brydon125's point is that /(J->F) does not strictly require that J and /F be true. J and /F is an interesting case, and a possibility for something that could be true under /(J->F), and in a way that's different than under J->F, but J and /F is not a logical consequence of /(J->F), and cannot be assumed.
@businessgoose Though I think I realized where the authors' confusion may have come from. In a few lessons from now we look at negating the statement "All X-Wings have hyperdrives." If we translate that into Lawgic we might say
X -> H
If we negate that we'll get
/(X->H)
Which is "not all X-Wings have Hyperdrives." And this DOES require that there is one X-Wing that does not have a Hyperdrive, which would be X and /H.
But this is a consequence of the English. If the original statement was "All X-Wings must have Hyperdrives" we'd end up with "It is not the case that all X-Wings must have Hyperdrives." This case does NOT require that an X-Wing without a Hyperdrive must exist, but it does allow for the case.
I think there was some early lesson in Foundations in which J.Y. said something like "subset relationships aren't exactly like conditionals, but for the LSAT you don't need to know the difference." This may be true, but I think this example that the 7Sage authors chose may be breaking that rule.
@iamorganized This issue can come up in quite a few places.
For example, let's say we have a Must Be True question (asking us to pick the answer that MBT based on the given facts). THe stimulus might say:
"Some people think if A is true, B must be true. But that's false."
In that case, the correct answer is likely to come from the idea that "If A, B" is not true. The correct answer might say, "It's possible to have A, but not have B."
Or in an argument-based question, the conclusion might be something like "But the critics are wrong." And to understand that, we have to understand what the critics said. The critics might have said a conditional "All Xs are Y." So to understand what the conclusion means (the critics are wrong), we need to understand that the negation of "All Xs are Y" is "Some Xs are NOT Y."
This is one of the more advanced things the LSAT will require us to do, so it doesn't come up that often. But you'll want to understand how to negate or contradict a conditional on maybe a handful of questions per test.
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.
@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?
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)?
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156 comments
"To be a Jedi, one must not be able to use the Force" melted my brain so hard
Is saying A can not occur and B can occur (/A and B) still a negation of the conditional instead of saying A can occur and B not occur (A and /B)?
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
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..?}
can someone explain how this type of negation is not a mistaken negation? How come when we're originally taught about contrapositives, we flip and negate, and for these relationships that's now incorrect?
@gbeeven because this is for negation not contrapositives. A user named Johnathan Kailey has a good explanation below.
@ShortBee that helped sm!! thank u!
@gbeeven Negation of a relationship between two claims is not the same thing as taking the contrapositive of a concept.
The contrapositive of A --> B is /B --> /A...these two statements are logically equivalent.
The negation of A --> B is that just because A happens, that does not necessarily mean B has to happen.
Example: To pass the bar, one must be a lawyer.
Negation: It is not the case that to pass the bar, one must be a lawyer.
Lawgic: pass bar --> be lawyer
pass bar and /be lawyer
the trap is definitely trapping
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
What does /(A->B) mean
@mattiesas the negation of the whole relationship!
Just like how /A meant the negation of a single condition, the parenthesis show that the negation in /(A->B) applies to the whole relationship rather than just one condition.
IS this a correct negation?
You can be a Jedi but not be able to use the Force
It is not necessary to be a Jedi to use the force
Is that correct? Flows better to me
@CarlosHernandez03 I'm not entirely certain that that is correct, as our goal in this negation is to deny the conditional relationship; that is, we're trying to say, "We can be A without being B." I believe your statement is saying, "You don't have to be A in order to be B."
The statement, "It is not necessary to be a Jedi to use the force," does not deny the conditional relationship as it is saying, "It is not necessary to be a Jedi to use the force, but you can still be a Jedi and use the force." Therefore, it is not outright denying this conditional relationship, as we're aiming for in negation.
The phrase, "It's not the case that to be a Jedi, one must be able to use the Force," does deny this conditional relationship because it's outright shutting down the idea that there's any causation between Jediship and Force use. "It is not necessary to be a Jedi to use the force," is instead drawing a line in the sand amongst Force users while not denying this causation. Negation is aiming to deny this causation; it's aiming to deny this conditional relationship.
I hope this makes even a lick of sense; logic is incredibly hard to express in English, and I sincerely hope this doesn't come across condescending or overly-corrective in any way! Please give any feedback or thoughts you have!! Have a wonderful day and good luck on your studies!!
I can't seem to understand the difference between negating "all" statements and negating conditional statements. Isn't All A are B (A->B) logically equivalent to If A then B (A-> B)?
@KhushyMandania I was a bit confused by as well as the Lawgic translations are the same but the main difference is the difference in relation it gives between two concepts.
You can see the differences in the negations of each. All A are B is simply stating that relation, for example "All games are fun" so we see with the negation when we deny that relationship we are stating that "it isn't the case that all games are fun" or "Some A are not B" so "Some games are not fun"
Now the difference in a conditional statements is the relationship between the two concepts is different, we are not saying that "All of A is B." We are instead saying "If A happens then B."
Therefore when we deny that relationship in the negation we see the differences there as well. Stating the A is independent of be or "A can occur and B not occur."
"If I find a game is fun then I will play it with my friends"
negation
"One can find a game fun and not play it with friends"
@DouglasNeumeyer Thanks so much for the clarification. It was super helpful!!
@KhushyMandania The difference is just about whether you are negating the conditional relationship (stating that it is not the case that A is sufficient for B) or negating the "all" statement (stating that it is not the case that ALL members of set A belong to set B). If we take the example of sentence "All dogs are cute" to illustrate this point, if we want to negate the conditional relationship in this sentence, that is to state that it's not sufficient to be a dog in order to be a cute being, we therefore write in Lawgic that we have D conjunction ~C (D and ~C) . It's like saying: "Hey, here's a set in which I have a dog, and look, it's not cute.) Alternatively, if we want to negate the quantifier ALL, meaning that we want to state that NOT ALL dogs are cute, we are therefore saying that some dogs are not cute, which we express in Lawgic by writing D < -- s -- > ~C. So, for all practical purposes, whether we are going to use one kind of negation or the other depends purely on what instructions are we given in English.
@Stannis Ah I get it! thanksss
Isn't it inaccurate to say that /(A->B) translates to A ^/B?
Like, /(A->B) does NOT imply A. It could be /A.
We could still say that if /(A -> B) then A^/B could be true, but there is not a biconditional between the two statements.
It is true that A^/B -> /(A -> B) though.
@brydon125 Hey ! Could you specify what you mean here? Are you saying that /(A->B) should be /A and B, as opposed to A and /B? I was also a bit confused as to how we're distributing out the contrapositive, but I feel like the statement is correct whichever way, as long as they don't go together, since that's what we're trying to demonstrate.
@businessgoose I came by to see if anyone else had said what @brydon125 did. I think @brydon125's point is that /(J->F) does not strictly require that J and /F be true. J and /F is an interesting case, and a possibility for something that could be true under /(J->F), and in a way that's different than under J->F, but J and /F is not a logical consequence of /(J->F), and cannot be assumed.
@businessgoose Though /(A->B) IS a logical consequence of the truth of A and /B.
(A and /B) -> /(A->B)
@businessgoose Though I think I realized where the authors' confusion may have come from. In a few lessons from now we look at negating the statement "All X-Wings have hyperdrives." If we translate that into Lawgic we might say
X -> H
If we negate that we'll get
/(X->H)
Which is "not all X-Wings have Hyperdrives." And this DOES require that there is one X-Wing that does not have a Hyperdrive, which would be X and /H.
But this is a consequence of the English. If the original statement was "All X-Wings must have Hyperdrives" we'd end up with "It is not the case that all X-Wings must have Hyperdrives." This case does NOT require that an X-Wing without a Hyperdrive must exist, but it does allow for the case.
I think there was some early lesson in Foundations in which J.Y. said something like "subset relationships aren't exactly like conditionals, but for the LSAT you don't need to know the difference." This may be true, but I think this example that the 7Sage authors chose may be breaking that rule.
@ToweringTextbooks Thank you for writing out this reply/explanation!! The specification really helps.
can someone let me know what is the significance of this : ' (
@iamorganized This issue can come up in quite a few places.
For example, let's say we have a Must Be True question (asking us to pick the answer that MBT based on the given facts). THe stimulus might say:
"Some people think if A is true, B must be true. But that's false."
In that case, the correct answer is likely to come from the idea that "If A, B" is not true. The correct answer might say, "It's possible to have A, but not have B."
Or in an argument-based question, the conclusion might be something like "But the critics are wrong." And to understand that, we have to understand what the critics said. The critics might have said a conditional "All Xs are Y." So to understand what the conclusion means (the critics are wrong), we need to understand that the negation of "All Xs are Y" is "Some Xs are NOT Y."
This is one of the more advanced things the LSAT will require us to do, so it doesn't come up that often. But you'll want to understand how to negate or contradict a conditional on maybe a handful of questions per test.
@Kevin_Lin Ohhh I see thank you!
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
@VanillaCat ooo i like this 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?
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?
@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
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).
@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.
@ktacklesthelsat yes still wondering about this question.
@MPFerrari right!? :(
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)?
@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