How to negate conditional statements? Forum

[ioannisk]

I pulled some examples I had trouble with. How do you negate?:

1. All young people enetering the job market are highly trained professionals
2.if vapors toxic to humans are produced by the degradatin of household cleaning products by bacteria in any landfill, then the hleath of at least some humans suffer
3. If a practice involves the exposure of human vapors from household cleaning products, then it causes at least some damage to human health

4. converting a landfill into a public park will cause no damage to human health unless toxic vapors are produced in that landfill and humans are exposed to them

5. When landfills are converted to public parks, measures could be taken that would prevent people using the parks from beign exposed to toxic vapors.

Could you explain your thought process behind negating? Thanks!

[WaltGrace83]

I pulled some examples I had trouble with. How do you negate?:

1. NOT All young people enetering the job market are highly trained professionals (some young people entering the job market are NOT highly trained professionals)
2.if vapors toxic to humans are produced by the degradatin of household cleaning products by bacteria in any landfill, then the health of NO humans suffer

You can negate this in a few ways I suppose, but that's what would probably be tested on ^

3. If a practice involves the exposure of human vapors from household cleaning products, then it causes NO damage to human health

Same as above ^

4. converting a landfill into a public park will cause SOME damage to human health unless toxic vapors are produced in that landfill and humans are exposed to them

5. When landfills are converted to public parks, measures CANNOT BE taken that would prevent people using the parks from beign exposed to toxic vapors.

Could you explain your thought process behind negating? Thanks!

Someone will have to chime in with their thought process as I am going to botch the explanation and get you confused.

[jk148706]

I pulled some examples I had trouble with. How do you negate?:

1. NOT All young people enetering the job market are highly trained professionals (some young people entering the job market are NOT highly trained professionals)
2.if vapors toxic to humans are produced by the degradatin of household cleaning products by bacteria in any landfill, then the health of NO humans suffer

You can negate this in a few ways I suppose, but that's what would probably be tested on ^

3. If a practice involves the exposure of human vapors from household cleaning products, then it causes NO damage to human health

Same as above ^

4. converting a landfill into a public park will cause SOME damage to human health unless toxic vapors are produced in that landfill and humans are exposed to them

5. When landfills are converted to public parks, measures CANNOT BE taken that would prevent people using the parks from beign exposed to toxic vapors.

Could you explain your thought process behind negating? Thanks!

Someone will have to chime in with their thought process as I am going to botch the explanation and get you confused.

titcr

[ioannisk]

I pulled some examples I had trouble with. How do you negate?:

1. NOT All young people enetering the job market are highly trained professionals (some young people entering the job market are NOT highly trained professionals)
2.if vapors toxic to humans are produced by the degradatin of household cleaning products by bacteria in any landfill, then the health of NO humans suffer

You can negate this in a few ways I suppose, but that's what would probably be tested on ^

3. If a practice involves the exposure of human vapors from household cleaning products, then it causes NO damage to human health

Same as above ^

4. converting a landfill into a public park will cause SOME damage to human health unless toxic vapors are produced in that landfill and humans are exposed to them

5. When landfills are converted to public parks, measures CANNOT BE taken that would prevent people using the parks from beign exposed to toxic vapors.

Could you explain your thought process behind negating? Thanks!

Someone will have to chime in with their thought process as I am going to botch the explanation and get you confused.

When it's a conditional, you only cahnge the necessary part?

And when you make a change regarding all negotiations, you only take "one-step"

How do you reduce "Most"

I saw you reduced ALl to "Not All", I thought reducing it to Most would make sense?

[1Lin2015]

If you know how to diagram conditional statements, then negating them is quite easy.

Suppose you're given A --> B. The negation is A --> not B, or, via the contrapositive, B --> not A.

[1Lin2015]

I would suggest not worrying about the levels. That is, not all is the correct negation to all. Remember that most and some both include the possibility of all. Thinking about it this way will allow you to adapt to answer choices by finding what would constitute a logically equivalent quantifier. For example, not all is equivalent to some are not since they both mean "at least one is not".

[WaltGrace83]

I pulled some examples I had trouble with. How do you negate?:

1. NOT All young people enetering the job market are highly trained professionals (some young people entering the job market are NOT highly trained professionals)
2.if vapors toxic to humans are produced by the degradatin of household cleaning products by bacteria in any landfill, then the health of NO humans suffer

You can negate this in a few ways I suppose, but that's what would probably be tested on ^

3. If a practice involves the exposure of human vapors from household cleaning products, then it causes NO damage to human health

Same as above ^

4. converting a landfill into a public park will cause SOME damage to human health unless toxic vapors are produced in that landfill and humans are exposed to them

5. When landfills are converted to public parks, measures CANNOT BE taken that would prevent people using the parks from beign exposed to toxic vapors.

Could you explain your thought process behind negating? Thanks!

Someone will have to chime in with their thought process as I am going to botch the explanation and get you confused.

When it's a conditional, you only cahnge the necessary part? I don't think you can ONLY change the necessary part but I think not doing it that way would be HIGHLY unusual for the LSAT. Someone correct me if I am wrong. I suppose you might be able to negate the sufficient I just don't know how that would exactly work.

And when you make a change regarding all negotiations, you only take "one-step" If you mean you only do ONE negation, you are correct.

How do you reduce "Most" Do you mean NEGATE most? Most is a bit tricky to think about but if ~(most) then it is equal to (50% or less)

I saw you reduced ALl to "Not All", I thought reducing it to Most would make sense? This is an unsupported inference. If "not all" we don't know if its most. Let;s say we are selecting 100 people for a committee. If I say "all people are selected" and I want to negate it it would turn into "Not all people are selected." Now what does this mean? Well we actually don't know raw numbers anymore. "Not all" could mean I selected 99/100 people but it can also mean I selected 1/100 people. However "all" will NEVER be negated to "most." "All" is the equivalent to "not some" (some will NOT be selected) or "not all" (not everyone will be selected)

[ioannisk]

I pulled some examples I had trouble with. How do you negate?:

1. NOT All young people enetering the job market are highly trained professionals (some young people entering the job market are NOT highly trained professionals)
2.if vapors toxic to humans are produced by the degradatin of household cleaning products by bacteria in any landfill, then the health of NO humans suffer

You can negate this in a few ways I suppose, but that's what would probably be tested on ^

3. If a practice involves the exposure of human vapors from household cleaning products, then it causes NO damage to human health

Same as above ^

4. converting a landfill into a public park will cause SOME damage to human health unless toxic vapors are produced in that landfill and humans are exposed to them

5. When landfills are converted to public parks, measures CANNOT BE taken that would prevent people using the parks from beign exposed to toxic vapors.

Could you explain your thought process behind negating? Thanks!

Someone will have to chime in with their thought process as I am going to botch the explanation and get you confused.

When it's a conditional, you only cahnge the necessary part? I don't think you can ONLY change the necessary part but I think not doing it that way would be HIGHLY unusual for the LSAT. Someone correct me if I am wrong. I suppose you might be able to negate the sufficient I just don't know how that would exactly work.

And when you make a change regarding all negotiations, you only take "one-step" If you mean you only do ONE negation, you are correct.

How do you reduce "Most" Do you mean NEGATE most? Most is a bit tricky to think about but if ~(most) then it is equal to (50% or less)

I saw you reduced ALl to "Not All", I thought reducing it to Most would make sense? This is an unsupported inference. If "not all" we don't know if its most. Let;s say we are selecting 100 people for a committee. If I say "all people are selected" and I want to negate it it would turn into "Not all people are selected." Now what does this mean? Well we actually don't know raw numbers anymore. "Not all" could mean I selected 99/100 people but it can also mean I selected 1/100 people. However "all" will NEVER be negated to "most." "All" is the equivalent to "not some" (some will NOT be selected) or "not all" (not everyone will be selected)

I thought for negating conditionals, make the necessary condition simply say "No" is wrong, and the correct negation would involve "Not necessarily"

[Christine (MLSAT)]

Ahhhh, the often misunderstood 'negating of a conditional'.

I'm afraid that I'm on a phone, so this will necessarily be a bit less robust than my usual response.

What is a conditional statement? It's a rule! Imagine two little kids on the playground. One says: "If you step on the yellow line, you're out of the game!" The second little kid says "NUH UH, that's not a RULE!"

This is the essense of negating a conditional. It's critical to keep in mind that the negation of a conditional IS NOT ITSELF A CONDITIONAL. Instead, you are saying "this rule isn't a rule", or "this trigger does not always produce that result".

If you have a statement "All A are B" and you want to be that NUH UH kid, you're going to saying that 'NOT all A are B'. In other words, "some A are not B". Similarly, the conditional statement (equivalent) "If A--> B" would be negated by saying "the trigger A does NOT ALWAYS lead to the result B".

You don't need to guarantee that it NEVER leads to the result (which is what "IF A --> not B" suggests), but rather that it just doesn't *always* work that way.

Remember: negating conditionals is being the kid on the playground that says "NUH UH, that's not a RULE - you just made that up!"





EDITED because words are hard.

[Christine (MLSAT)]

Hey WaltGrace83! Mind if I tweak a bit? These are close, but some of them are trying too hard to be definitive conditional statements of their own.

On some questions the distinction won't ruin you, but it's important to be careful with this kind of thing.

I pulled some examples I had trouble with. How do you negate?:

1. NOT All young people enetering the job market are highly trained professionals (some young people entering the job market are NOT highly trained professionals)

Totally agree with this.

2.if vapors toxic to humans are produced by the degradatin of household cleaning products by bacteria in any landfill, then the health of NO humans suffer

You can negate this in a few ways I suppose, but that's what would probably be tested on ^

Actually, you need to only account for the *possibility* that no humans suffer. So:

If vapors are produced, it's possible that no human's health will suffer.

3. If a practice involves the exposure of human vapors from household cleaning products, then it causes NO damage to human health

Same as above ^


Same tweak as above

4. converting a landfill into a public park will cause SOME damage to human health unless toxic vapors are produced in that landfill and humans are exposed to them

Same tweak: "converting a landfill into a public park MAY cause damage.

5. When landfills are converted to public parks, measures CANNOT BE taken that would prevent people using the parks from beign exposed to toxic vapors.

same tweak: When landfills are converted, measure MAY NOT BE ABLE TO BE TAKEN to prevent...

Could you explain your thought process behind negating? Thanks!

Someone will have to chime in with their thought process as I am going to botch the explanation and get you confused.

Negating a conditional will mean that the result doesn't follow in all cases of the trigger!

[WaltGrace83]

Droppin' the knowledge bomb ^. I was so close! I didn't know that distinction existed so thanks for that!

[WaltGrace83]

Wait a second (sophomore year logic class came screaming back to me)...

A→B. To negate that it is just ~(A→B). Thus, you are just saying that A doesn't have to lead to B. A could lead to ~B too. Thus, if you get A, you don't really know anything if you come at it from the viewpoint of ~(A→B). However, not knowing anything doesn't necessarily mean that B or ~B is wrong or right. Is that the thought process?

...that was probably super confusing.

[ioannisk]

Wait a second (sophomore year logic class came screaming back to me)...

A→B. To negate that it is just ~(A→B). Thus, you are just saying that A doesn't have to lead to B. A could lead to ~B too. Thus, if you get A, you don't really know anything if you come at it from the viewpoint of ~(A→B). However, not knowing anything doesn't necessarily mean that B or ~B is wrong or right. Is that the thought process?

...that was probably super confusing.

it was kinda? i think you got the gist? i think i got it. Negating conditional statements (such as a-->b) is just simply saying A does not necessarily imply B, which means B could happen or not happen, its just not guranteed to happen

[Christine (MLSAT)]

Wait a second (sophomore year logic class came screaming back to me)...

A→B. To negate that it is just ~(A→B). Thus, you are just saying that A doesn't have to lead to B. A could lead to ~B too. Thus, if you get A, you don't really know anything if you come at it from the viewpoint of ~(A→B). However, not knowing anything doesn't necessarily mean that B or ~B is wrong or right. Is that the thought process?

...that was probably super confusing.

That's exactly it! That negation (~) lives OUTSIDE the parentheses, and is thus saying "no! That rule isn't a rule!"

Rules (conditionals) are trying to say we KNOW something for sure. Negating the conditional takes away that 'knowing'! If A occurs....we don't know squat!

[WaltGrace83]

Wait a second (sophomore year logic class came screaming back to me)...

A→B. To negate that it is just ~(A→B). Thus, you are just saying that A doesn't have to lead to B. A could lead to ~B too. Thus, if you get A, you don't really know anything if you come at it from the viewpoint of ~(A→B). However, not knowing anything doesn't necessarily mean that B or ~B is wrong or right. Is that the thought process?

...that was probably super confusing.

it was kinda? i think you got the gist? i think i got it. Negating conditional statements (such as a-->b) is just simply saying A does not necessarily imply B, which means B could happen or not happen, its just not guranteed to happen

that made me lol. I was trying to think about it in a formal way like when I first learned logic.

[WaltGrace83]

I revisited a question from awhile ago and thought about this thread so I thought I'd update it with my thoughts and maybe it will bring to light these ideas more thoroughly (or just show that I never knew what I was talking about ). I would try to narrow the core down to less words but I am afraid of missing something important.

34.3.17 "Zoologist: animals can certainly signal each other..."

• (Animals signaling each other with sounds or gestures) does not prove the ability to use them to refer to concrete objects or abstract ideas
  →
  (Animals signaling each other with sounds or gestures) does not confirm that animals possess language

Assumption: To confirm language, one must prove ability to refer to concrete objects or abstract ideas

Now onto why I thought about negating conditionals...

• (C) (Signaling with sounds or gestures → Refer to ~CO & ~AI). If we negate this, we get ~(Signaling with sounds or gestures → Refer to ~CO & ~AI). This would mean that we don't know what happens when the animals signal with sounds or gestures. We don't know what they refer to, if anything. This is certainly problematic because we do need to know something about what they are referring to. If we don't anything, then it is just as likely that we destroy the argument or help the argument.
  
  • -If we said that the animals AREN'T referring to (Concrete Objects) or (Abstract Ideas) then this would actually help the argument, making it less likely that the animals possess language.
    -If we said that the animals ARE referring to (Concrete Objects) or (Abstract Ideas) then this would actually hurt the argument, making it more likely that the animals possess language.
  
  This is of course all working under the assumption that referring to concrete objects or abstract ideas is something necessary for language (what D would later get to).
  
  (D) However, works a little bit differently. (System of sounds or gestures doesn't contain expressions referring to concrete objects or abstract arguments → ~Language). If we negate this, we get the following: ~(System of sounds or gestures doesn't contain expressions referring to concrete objects or abstract arguments → ~Language). So what this means is that the "System of sounds or gestures that doesn't contain expressions referring to concrete objects or abstract arguments" could be either a language or not a language.
  
  Why is this problematic for the argument? This is problematic because the argument definitely says that the sounds or gestures does not confirm that animals possess language, period. By showing that the system of sounds or gestures MAY or MAY NOT confirm the animals language then we are in serious doubt of the conclusion. Basically, we have no reason to believe (or not believe) the conclusion. Thus, the conclusion does not follow from the premises and that is exactly what we are trying to find when we negate an answer choice. (D) is correct.

How does that look, guys and girls?

• • I'll knock out the less relevant ones only for completeness sake.
    
    • (A) They could totally have the cognitive abilities but the key is to prove whether or not they use sounds/gestures to refer to those abstract ideas
      
      (B) Once again, we don't care about "entertaining," we want to see how signaling ties in to those abstract ideas
      
      (E) This would have probably been right if it would have said "Some animals that possess a language can refer to either concrete objects or abstract ideas." However, it is not necessary to be able to refer to both.

[LSAT Hacks (Graeme)]

"No! That isn't a rule!" is the right way to think about negations.

Further, you want to think about something not being a rule in the slightest way possible. I find having an intuitive conception of this helps more than figuring out the specific wording.

Statement: All Americans are nice

Negation: Some americans are not nice

How I actually think about it: One guy in Arkansas, Bob, is a jerk. All other Americans are nice

----

Statement: If a practice involves the exposure of human vapors from household cleaning products, then it causes at least some damage to human health

Negation: This practice doesn't always cause some damage to human health

How I think about it: This practice always harms health, except in one case where a guy inhaled a tiny amount of a non-toxic vapor and was ok

-----

Now, why do I think about negations in that way? Because it shows that those negations are REALLY not powerful. A negation of a necessary statement will DESTROY the argument. One jerk in Arkansas isn't significant or one case of safe vapors is not significant.

Whereas, if I am arguing that the nuclear power plant is safe because of the backup system, then "the backup system may fail" is a worrying negation of the condition "the backup never fails".