It took me a REALLY long time to think this through:
Being in Los Angeles (subset) is sufficient to know you're in California (superset), but being in Los Angeles (subset) is not necessary for knowing you're in California (superset). You don't necessarily need to know that you're in Los Angeles in order to know you're in California; you could be in San Diego, Sacramento, or San Jose. As long as you are in California, it's not necessary to know WHERE EXACTLY you are in California, in order to know you're already in California.
Let's say the border of California was equipped with a high-tech alarm system that would blare sirens and absolutely let you know that you walked into the ocean/Oregon/Nevada/Arizona. And let's say you were blind-folded, dropped into the center of California, and told to walk around randomly in any direction for 3 hours. At the end of those 3 hours, you stop walking, and you know for a fact that the alarm never went off during your 3 hour walk. You know you never left California because the sirens never blared. So you have to KNOW you're in California, even though you have no clue what part of the state you're in. Are you north? Are you south? Doesn't matter. That's what it means by: "subset membership is not necessary for superset membership". Knowing you're in Los Angeles is not necessary for knowing you're in California.
What is the best way to break it down like sufficient (is not required) and necessary (is required)?
Would this be a good way to think about it without too many moving parts? For instance, using an LSAT prep example:
7Sage (A) is a subset of LSAT course prep (B), which is the superset. This means that 7Sage (A) is sufficient to imply you are taking an LSAT prep course (B).
However, it is not necessary to take 7Sage (A) to be in LSAT prep (B), because LSAT prep can also include other methods, such as a college class or a private tutor.
Being in LSAT prep (B) is necessary in order to be using 7Sage (A), because every instance of 7Sage falls within LSAT prep.
@isabellagirjikian Your example is spot on, but the "is" and "is not required" I think introduces negatives ("not") which might make things confusing. I've thought about this a bit and way I use familiar language to wrap my head around is:
sufficient means "guarantees" and necessary means "required to be eligible" to wrap my head around it most when thinking about what each does and does not prove.
example:
Taking 7Sage guarantees (is sufficient for) taking an LSAT course prep. & not taking 7Sage does not guarantee anything about taking an LSAT course prep.
Taking an LSAT course prep gives you eligibility (is necessary for) to be taking 7Sage. & not taking an LSAT course prep makes you ineligible for taking specified 7Sage.
I think the final list of conditions helped me really nail down why something that is necessary is not sufficient. Necessary is if A, then B guaranteed. Flipping it around (If membership in mammal-set), made me understand why it wouldn't be sufficient.
If anyone else is having issues with this distinction, think of this. Sufficient: It is something that assures me Y is going to happen. Necessary: It is something that is required for X to happen. So, think about getting a good score in the LSAT, is it the only thing I need (sufficient) to get in the T4 law schools? No, but it is required (necessary).
IRL analogies make things feel more intuitive, but get used to not thinking in reality as much. Think about what the question is giving you.
Take this as true: If you are in your bedroom, then you must be in your apartment.
Then this is confusing the suff/nec conditions:If you are in your apartment, then you must be in your bedroom.
In the world you made, the only acceptable logic is -
Bedroom -> Apartment
/Apartment -> /Bedroom
Unless you live in NYC, then your apartment is also likely your bedroom. lol
But the stims will not always operate in reality/intuition. You have to live in what the question is telling you is true. If it says that it is true that all bananas are blue, you have to live in that world.
@LaurenBarthel This is pretty good. I think a sharper way to express the relationship using your analogy is this -
Jane is baking a cake. She has gathered her ingredients and added everything to the bowl, creating a batter. Jane poured the batter into the baking pan before placing it in the oven. Heating the oven prior to putting the filled cake pan in the oven is important for the cake to bake, so she also did that before mixing ingredients. Ovens that are not preheated do not make good cakes. The oven must be preheated if Jane wants to bake a good cake.
1) If Jane wants to bake a good cake, the oven must be preheated.
2) If the oven is preheated, Jane must be baking a good cake.
1 restates the conclusion. Preheating the oven is a necessary condition to bake a good cake. This makes intuitive sense, but also is just a restatement of the relationship found in the argument.
2 confuses the necessary and sufficient conditions. You could be baking anything, it doesn't have to be a cake, or even a good one. So baking a good cake is not a necessary condition for the oven being preheated.
@LaurenBarthel Or even more directly - if we take everything we know to be true, flour can be used for any number of recipes, not just cakes. So it isn't a sufficient condition for baking a cake. Baking a cake is a sufficient condition for flour being needed. Baking a cake lives inside the "flour needed" circle the same way making fried chicken sits inside the "flour needed" circle.
More importantly, focus entirely on the world of the stimulus. You cannot rely on outside knowledge unless it's strongly reasonable to make that assumption. Baking a cake is intuitive, but LSAT questions are often very unintuitive or overly dense.
Okay, this stuff makes no sense to me. It feels like a completely foreign language. And the examples are just making it more confusing. Can someone explain this in a way more simple way?
@JasmineMinhas So going back to the USA NYC example.
With USA as the superset and NYC as the subset as we know it falls inside the USA.
Now look at the member within the subset of NYC, Empire State Building. This member is "sufficient" enough to fall under both NYC and USA as you know the empire state building is both in NYC which is also in the USA.
BUT there are other landmarks in the USA other than the Empire State Building (i.e. Golden Gate Bridge, Grand Canyon) things that can fall in the superset of USA but not NYC. So the Empire State building is "sufficient" enough to fall under both USA and NYC but not "necessary" to be a member of the broader superset of USA.
I feel (including myself) got confused that the Empire State Building being "not necessary" as you'd think "Oh obviously it necessary because the Empire State Building is in NYC and USA so why wouldn't it be necessary" I kept getting hung up on the verbiage of "not necessary."
The way I helped my head wrap around this concept better was looking at it from the perspective of the Eiffel Tower.
The Eiffel Tower is in no way inside the USA so we know 100% that it could never fall inside the subset of NYC. Therefore we know for sure that if a member is to fall outside the superset of the USA that for sure means (or it is a "necessity" and not "sufficient" enough) to ever fall into the subset of NYC.
Hopefully that helps at least a little, I'm still trying to fully grasp it myself.
Honestly, I had a decent understanding of sufficiency and necessity before this video and this just confused the heck out of me. Am I the only one? Maybe too many moving parts.
@jrm98 Yes, that is the way I grasped the lesson. Example. If something is a dog, then it is an animal - sufficient. Whereas, But somehting can be animal without being a dog - necessary
I like this explanation the most, so here is like an example I came up with
It is "required"(necessary) that you have Internet to use Instagram
But it is not "enough" (sufficient) to only have the Internet to use Instagram, you also need a smart phone with battery to use Instagram lol 😅
So in this example
When I say Jesse is using Instagram
The "necessary" condition is: Jesse has Internet
Jesse using Instagram is the subset inside the circle of Jesse has Internet
However when I ask how is Jesse using the Internet
Using Instagram is sufficient (enough) but not necessary (required)
It could be the case that Jesse is using the Internet to study on 7Sage, here studying 7Sage is sufficient (enough) but also not required (necessary) of Jesse to use the Internet
The way it is laid out in the arrow example of Super set Necessary subset. was initially confusing. But i parsed it like this. You have to be (necessary) in the USA if you are in New York that must be true 100 percent of the time. However being in New York means you are in the USA (sufficient) But you do NOT HAVE to be (necessary) in New York to be in the USA. Maybe this will help someone
Eating shrimp is sufficient to eat Seafood, but not necessary.
Since shrimp is a subset (belonging to the seafood group) you can eat shrimp which would be sufficient enough to eating A SEAFOOD. BUT it is not necessary to eat ALL foods of seafood.
You can eat from the specific (shrimp) which is a subset of seafood which is a general group, but it is not necessary.
Eating seafood is necessary to eat shrimp, but not sufficient.
If you are in the superset of seafood, that must mean it is necessary to eat shrimp. Shrimp is a specific item of seafood.
But it is not sufficient to just eat shrimp. If you eat seafood, it is not sufficient that you are eating shrimp. You don't have to eat shrimp, but it is necessary that you eat a seafood.
Another Example:
The city of Houston is sufficient to be in the USA, but not Necessary.
Living in the city of Houston is specific, sufficient, and JUST ENOUGH to be in the United States, BUT NOT NECESSARY.
You can live in any city and still be in the USA. It is not necessary to live in Houston, if you want to be in the United States you can live in NYC, LA, etc.
The country of USA is necessary to be in the city of Houston, but not sufficient.
Living in the USA is necessary if you want to live in the city of Houston but is not sufficient.
But it is not sufficient to just live in Houston. You can live in any city and be in the USA, as long as the city is located in the USA.
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184 comments
this is not necessarily on the topic of s v n but the way that JY talks is so perfect for my ADHD brain i cant explain why but it helps so much LMAO
subset is to superset as sufficiency is to necessity ... this COMPLETELY blew my mind. ty :)
It took me a REALLY long time to think this through:
Being in Los Angeles (subset) is sufficient to know you're in California (superset), but being in Los Angeles (subset) is not necessary for knowing you're in California (superset). You don't necessarily need to know that you're in Los Angeles in order to know you're in California; you could be in San Diego, Sacramento, or San Jose. As long as you are in California, it's not necessary to know WHERE EXACTLY you are in California, in order to know you're already in California.
Let's say the border of California was equipped with a high-tech alarm system that would blare sirens and absolutely let you know that you walked into the ocean/Oregon/Nevada/Arizona. And let's say you were blind-folded, dropped into the center of California, and told to walk around randomly in any direction for 3 hours. At the end of those 3 hours, you stop walking, and you know for a fact that the alarm never went off during your 3 hour walk. You know you never left California because the sirens never blared. So you have to KNOW you're in California, even though you have no clue what part of the state you're in. Are you north? Are you south? Doesn't matter. That's what it means by: "subset membership is not necessary for superset membership". Knowing you're in Los Angeles is not necessary for knowing you're in California.
What is the best way to break it down like sufficient (is not required) and necessary (is required)?
Would this be a good way to think about it without too many moving parts? For instance, using an LSAT prep example:
7Sage (A) is a subset of LSAT course prep (B), which is the superset. This means that 7Sage (A) is sufficient to imply you are taking an LSAT prep course (B).
However, it is not necessary to take 7Sage (A) to be in LSAT prep (B), because LSAT prep can also include other methods, such as a college class or a private tutor.
Being in LSAT prep (B) is necessary in order to be using 7Sage (A), because every instance of 7Sage falls within LSAT prep.
@isabellagirjikian Your example is spot on, but the "is" and "is not required" I think introduces negatives ("not") which might make things confusing. I've thought about this a bit and way I use familiar language to wrap my head around is:
sufficient means "guarantees" and necessary means "required to be eligible" to wrap my head around it most when thinking about what each does and does not prove.
example:
Taking 7Sage guarantees (is sufficient for) taking an LSAT course prep. & not taking 7Sage does not guarantee anything about taking an LSAT course prep.
Taking an LSAT course prep gives you eligibility (is necessary for) to be taking 7Sage. & not taking an LSAT course prep makes you ineligible for taking specified 7Sage.
I think the final list of conditions helped me really nail down why something that is necessary is not sufficient. Necessary is if A, then B guaranteed. Flipping it around (If membership in mammal-set), made me understand why it wouldn't be sufficient.
If A is a subset of B, then being in A is sufficient to imply you are in B.
It is not necessary to be in A to be in B because B may include other members outside of A.
Being in B is necessary in order to be in A, because every member of A lies within B
@LaurenJ24 Good explanation, thank you! :)
If anyone else is having issues with this distinction, think of this. Sufficient: It is something that assures me Y is going to happen. Necessary: It is something that is required for X to happen. So, think about getting a good score in the LSAT, is it the only thing I need (sufficient) to get in the T4 law schools? No, but it is required (necessary).
first time commenting. just have to say i'm beyond confused lol hoping it'll get clearer as I go on
@BrittanyJohnson Good luck, my friend, you got this!! you have the full force of all 7sage users supporting you 🙂↕️
This is so confusing
mind boggling lesson...
NECESSARY: being in my apartment to sleep in my bedroom.
SUFFICIENT: being in my bedroom to be in my apartment (I could be in any room.)
Did I get that right?
@AustinSanchez yeah.
IRL analogies make things feel more intuitive, but get used to not thinking in reality as much. Think about what the question is giving you.
Take this as true: If you are in your bedroom, then you must be in your apartment.
Then this is confusing the suff/nec conditions: If you are in your apartment, then you must be in your bedroom.
In the world you made, the only acceptable logic is -
Bedroom -> Apartment
/Apartment -> /Bedroom
Unless you live in NYC, then your apartment is also likely your bedroom. lol
But the stims will not always operate in reality/intuition. You have to live in what the question is telling you is true. If it says that it is true that all bananas are blue, you have to live in that world.
@gurbytown if the bananas are blue I must be in blue banana world. Haha
Thanks for the clarification!
Let me see if I'm understanding this.
Having flour is needed when baking a cake, but flour alone is not enough to bake a cake, as you need other ingredients.
This makes flour necessary to baking a cake, but not sufficient.
@LaurenBarthel This is pretty good. I think a sharper way to express the relationship using your analogy is this -
Jane is baking a cake. She has gathered her ingredients and added everything to the bowl, creating a batter. Jane poured the batter into the baking pan before placing it in the oven. Heating the oven prior to putting the filled cake pan in the oven is important for the cake to bake, so she also did that before mixing ingredients. Ovens that are not preheated do not make good cakes. The oven must be preheated if Jane wants to bake a good cake.
1) If Jane wants to bake a good cake, the oven must be preheated.
2) If the oven is preheated, Jane must be baking a good cake.
1 restates the conclusion. Preheating the oven is a necessary condition to bake a good cake. This makes intuitive sense, but also is just a restatement of the relationship found in the argument.
2 confuses the necessary and sufficient conditions. You could be baking anything, it doesn't have to be a cake, or even a good one. So baking a good cake is not a necessary condition for the oven being preheated.
@LaurenBarthel Or even more directly - if we take everything we know to be true, flour can be used for any number of recipes, not just cakes. So it isn't a sufficient condition for baking a cake. Baking a cake is a sufficient condition for flour being needed. Baking a cake lives inside the "flour needed" circle the same way making fried chicken sits inside the "flour needed" circle.
More importantly, focus entirely on the world of the stimulus. You cannot rely on outside knowledge unless it's strongly reasonable to make that assumption. Baking a cake is intuitive, but LSAT questions are often very unintuitive or overly dense.
@gurbytown You made it click for me thank you!!!
Okay, this stuff makes no sense to me. It feels like a completely foreign language. And the examples are just making it more confusing. Can someone explain this in a way more simple way?
@JasmineMinhas So going back to the USA NYC example.
With USA as the superset and NYC as the subset as we know it falls inside the USA.
Now look at the member within the subset of NYC, Empire State Building. This member is "sufficient" enough to fall under both NYC and USA as you know the empire state building is both in NYC which is also in the USA.
BUT there are other landmarks in the USA other than the Empire State Building (i.e. Golden Gate Bridge, Grand Canyon) things that can fall in the superset of USA but not NYC. So the Empire State building is "sufficient" enough to fall under both USA and NYC but not "necessary" to be a member of the broader superset of USA.
I feel (including myself) got confused that the Empire State Building being "not necessary" as you'd think "Oh obviously it necessary because the Empire State Building is in NYC and USA so why wouldn't it be necessary" I kept getting hung up on the verbiage of "not necessary."
The way I helped my head wrap around this concept better was looking at it from the perspective of the Eiffel Tower.
The Eiffel Tower is in no way inside the USA so we know 100% that it could never fall inside the subset of NYC. Therefore we know for sure that if a member is to fall outside the superset of the USA that for sure means (or it is a "necessity" and not "sufficient" enough) to ever fall into the subset of NYC.
Hopefully that helps at least a little, I'm still trying to fully grasp it myself.
@JasmineMinhas Not sure if this will help but found it easier to visualize this way.
If I am in my room (subset) I am in my apt (superset).
If I am in my room - that is sufficient info to know - that I am in my apt.
That said, I can be in my apt in a place that is not my room (like the kitchen or something). Just bc I am in my apt does not mean I am in my room.
Being in my apt is necessary for me to be in my room. So if I am not in my apt (superset), I know I cannot be in my room (subset).
I wanted to ask a clarifying question. Would a good way to understand this be
if in subset --> then in superset
then the negation:
if not in superset --> then not in subset
I am having a tough time understanding and applying and recognizing this concept on LSAT questions.
Also, would this be the case:
cat --> mammal
but NOT mammal --> cat
if someone said mammal --> cat, then this could be confusing sufficiency for necessity which is the oldest mistake in the book
is this correct?
Honestly, I had a decent understanding of sufficiency and necessity before this video and this just confused the heck out of me. Am I the only one? Maybe too many moving parts.
Um Garfield is a cartoon character. Cartoon characters do not produce living young, therefore Garfield is not a mammal, he only represents one.
I've struggled with sufficiency for some reason, so wrote out a couple things that helped -
Being in subset is sufficient for membership in superset.
If in subset, guaranteed in superset.
If in subset, must be in superset.
If in subset, necessarily in superset.
Being in superset is not sufficient for membership in subset.
If in superset, not guaranteed to be in subset.
If in superset, could be in subset.
If in superset, not necessarily in subset.
Sufficiency is like - is this information sufficient for me to believe another thing.
Claim: Jane lives in New York. Is that sufficient for me to assume she lives in the US? Yes it is sufficient.
Claim: Jane lives in the US. Is that sufficient for me to assume she lives in New York? No, it is not sufficient.
Claiming Jane lives in New York so she must live in US is valid. Must be true.
Claiming Jane lives in US so she must live in New York is not valid. Could be true.
@gurbytown wow this is a great example, thank you so much for sharing it!
@gurbytown Thanks for sharing this! :) having a second example helped with making sense of it.
@gurbytown amazing example, thank you for sharing it!
@gurbytown Excellent example, I wrote this in my notes. Thank you stranger
im slight confused .. someone please help me understand. this is what i broke it down into on my notes
if i am a cat then i am a mammal - sufficient
BUT
if i am a mammal, im not necessarily a cat. i can be a mammal without being a cat - necessary
like
if im in miami then im in florida - sufficient
BUT
if im in florida it doesnt necessarily mean that im in miami because i could be in orlando and still be in florida - neccesary
am i getting this right...??
@jrm98 Yes, that is the way I grasped the lesson. Example. If something is a dog, then it is an animal - sufficient. Whereas, But somehting can be animal without being a dog - necessary
@Sanni_3 thank you!!
Subset membership is enough for superset membership but not required. Superset membership is required for subset membership, but not enough.
@JesseMcCarthy
I like this explanation the most, so here is like an example I came up with
It is "required"(necessary) that you have Internet to use Instagram
But it is not "enough" (sufficient) to only have the Internet to use Instagram, you also need a smart phone with battery to use Instagram lol 😅
So in this example
When I say Jesse is using Instagram
The "necessary" condition is: Jesse has Internet
Jesse using Instagram is the subset inside the circle of Jesse has Internet
However when I ask how is Jesse using the Internet
Using Instagram is sufficient (enough) but not necessary (required)
It could be the case that Jesse is using the Internet to study on 7Sage, here studying 7Sage is sufficient (enough) but also not required (necessary) of Jesse to use the Internet
The way it is laid out in the arrow example of Super set Necessary subset. was initially confusing. But i parsed it like this. You have to be (necessary) in the USA if you are in New York that must be true 100 percent of the time. However being in New York means you are in the USA (sufficient) But you do NOT HAVE to be (necessary) in New York to be in the USA. Maybe this will help someone
sufficiency (subset) vs necessity (superset)
Eating shrimp is sufficient to eat Seafood, but not necessary.
Since shrimp is a subset (belonging to the seafood group) you can eat shrimp which would be sufficient enough to eating A SEAFOOD. BUT it is not necessary to eat ALL foods of seafood.
You can eat from the specific (shrimp) which is a subset of seafood which is a general group, but it is not necessary.
Eating seafood is necessary to eat shrimp, but not sufficient.
If you are in the superset of seafood, that must mean it is necessary to eat shrimp. Shrimp is a specific item of seafood.
But it is not sufficient to just eat shrimp. If you eat seafood, it is not sufficient that you are eating shrimp. You don't have to eat shrimp, but it is necessary that you eat a seafood.
Another Example:
The city of Houston is sufficient to be in the USA, but not Necessary.
Living in the city of Houston is specific, sufficient, and JUST ENOUGH to be in the United States, BUT NOT NECESSARY.
You can live in any city and still be in the USA. It is not necessary to live in Houston, if you want to be in the United States you can live in NYC, LA, etc.
The country of USA is necessary to be in the city of Houston, but not sufficient.
Living in the USA is necessary if you want to live in the city of Houston but is not sufficient.
But it is not sufficient to just live in Houston. You can live in any city and be in the USA, as long as the city is located in the USA.
hey, so i don't get it lol
This example was confusing to me :( Thank you to people in the comments for additional examples and breakdowns!
Being in the United States is necessary to be in NYC, but not sufficient.
Being in NYC is sufficient to be in the United States, but not necessary.
Because dogs.
This is a fantastic sentence.