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Omg, the example with the cats (in different classes) just FINALLY clicked for me!!!! I actually want to cry, I feel like my brain just unlocked a new power or something bc you literally broke down every single ELEMENT that I have been confused on for WEEKS. I want to give you a hug rn. (3(/p)

Denying the necessary Lets Us Conclude Things

Affirming the sufficient Lets Us Conclude Things I've literally been searching for an explanation like this wow.

So in the biology example, (copying it here so I can see it while typing lol):

**4: thorny seedpods -> curled leaves

This is where you went wrong - you did an "All Mammals are Cats" here. We have affirmed the necessary - we know that our specimen has curled leaves. However, this relationship is only saying that curled leaves are necessary for something to have thorny seedpods. Thorny seed pods, on the other hand, are merely SUFFICIENT for having curled leaves.

There may be other ways to get curled leaves, just like the statement

cats -> mammals

leaves room for other ways to be a mammal other than being a cat (which we happen to also know is true from our general knowledge.) In short - affirming the necessary doesn't let us conclude anything.**

So just because the necessary condition of curled leaves is affirmed, it means nothing for a conclusion because it did not give us "plant x has thorny seedpods" ? For example, if it had said that plant x had thorny seedpods (but did not say anything about curled leaves) then we could conclude it had curled leaves right? Because we are affirming the sufficient? (This is just me thinking out loud so i can make sure my reasoning is correct now)

I cannot thank you enough for this, you made me finally understand this and I am so so so so grateful for your extensive explanation and taking the time out of your day to do that :) I'm still mindblown rn at how that finally clicked for me... god i feel dumb lol

You've got it my friend!

You nailed it in the example you gave (i bolded for ease of reference)

for the relationship

thorny seedpods --> curled leaves

affirming the sufficient has the power for us to logically conclude that our specimen has curled leaves.

Affirming the sufficient and denying the necessary let us conclude things.

If you ever find this stuff feeling foggy again (it happens to me more often than I'd care to admit), you can go back to cats and mammals during your studies so that you can feel like you are on solid ground again.

It is my pleasure! I spent a long time trying to figure out what this stuff means in the past few months, and I had to turn it over in my head for a while to be able to define it. Also... typing it all out helped me, as it forced me to put some of this stuff into words and know it a bit better.

Good luck studying - you can do it!

I like to think about it in terms of cats and mammals whenever I get confused.

Bear with my analogy for a moment - I will answer your question about affirming the necessary further down in this, but stick with the cat metaphor for a bit. At the end, I will help to apply the cat analogy to the problem you're stuck on.

Please note - for this entire post, when I say CAT, I really mean "House Cat."

OK- Being a cat is sufficient for being a mammal.

Conversely, being a mammal is necessary for being a cat.

the relationship is written like this.

cats --> Mammals

we call the left thing the sufficient condition, because affirming it is SUFFICIENT for the condition on the right to be true. (/ug) (that is to say - if you are indeed a cat, its enough to make you a mammal, but its not guaranteed to be the only way to be a mammal)

we call the right thing the necessary condition, because affirming it is NECESSARY for the condition on the left to be true.(/ug)

If you put an animal in a bag and tell me its a mammal, I can't, however, logically deduce "Oh, it's a cat!".

That would just be flipping the relationship around arbitrarily.

mammal --> cat

You can't do this! Our general knowledge tells us why - There are tons of mammals that are NOT cats!

As you know, The conclusion of "all mammals are cats" is not implied from "all cats are mammals" . you'd be insane to conclude this. You just, simply put, can't work right to left. It leads you to saying pants on head stupid things like "Because it's a mammal, it's a cat." It is also extremely easy to do on accident, especially when under pressure or when there are deliciously tempting answer choices that APPEAR to give you what you are looking for (this is what happened in your problem, by the way. We've all done it a dozen times.)

OK, but, if you did want to go and work in the other direction, that is the contrapositive. Flipping and negating lets us preserve the truth of the original statement.

/mammal --> /cat

If you're not a mammal, you're for sure not a cat. Ok, yeah, that still works. Cool. This passes the reality check of our analogy.

Let's go deeper - here is that original, proper relationship expanded, so we have a bit more to work with.

All cats (again, house cats) are member of the family Felidae, and thereby also members of the order Carnivora, and thereby also members of the class of Mammal.

cat --> felidae --> carnivora --> mammal

Everything to the right of the cat is necessary for cat-ness. If it's a cat, its gotta be all of those. If I disprove any of those, ie, I say "Hey this animal in the bag is NOT a member of carnivora" then it's not a cat, because it HAS TO BE ALL THOSE things to be a cat.

If I tell you "the animal in the bag is a mammal" it is called "affirming the necessary". It doesn't tell us anything. It's a mammal? Cool, I guess, but in this relationship we have, it doesn't let me conclude anything. It could be a mammal, but not a member of Carnivora. Deer exist, and they are mammals, but not carnivores.

Saying "The animal in the bag is not a mammal" however, lets us validly conclude things. I know, 100% for a fact, that it is not a carnivora, not a felidae, and not a cat. This is called denying the necessary.

Let's consider sufficiency -

Being a cat (again, housecat) is SUFFICIENT for the stuff on the right. It doesn't guarantee that its the ONLY way, though. In fact, you and I happen to have real world knowledge that it is NOT the only way. There are other members of the genus felidae (tigers, lions, etc), other members of carnivora, and other kinds of mammals, or put differently in most arguments, there are other ways of achieving that end. Being a cat (housecat), however, is SUFFICIENT for being a member of felidae, being a member of carnivora, or being a member of mammal.

What if I did this?

What if I said the animal in the bag is not Felix the cat (housecat)?

Ok, well, let's look at our chain.

Felix (who is a cat) --> cat --> felidae --> carnivora --> Mammal

Ok, the animal in the bag isn't Felix. What can I say about the animal in the bag?

Uhhh..... Nothing, really. Just that it isn't Felix, but we already said that. It could still be a cat, just not Felix. This is denying the sufficient. It doesn't let us conclude anything.

If I say that the animal in the bag IS Felix the cat, though, I can validly conclude that the animal in the bag IS a cat, IS a felidae, IS a carnivora, and IS a mammal. This is affirming the sufficient.

important things to remember: Seriously, write these down and keep wrestling with them until you understand them. The rest of my post will help to illustrate a bit more, but you MUST feel comfortable with these concepts.

cats -> mammals

this statement says "Being a cat requires being a mammal."

we call the left thing the sufficient condition, because affirming it is SUFFICIENT for the condition on the right to be true. (/ug)

we call the right thing the necessary condition, because affirming it is NECESSARY for the condition on the left to be true. (/ug)

Denying the necessary and affirming the sufficient let you LOGICALLY CONCLUDE things. This is the "must be true" type of shit.

Affirming the necessary doesn't let us conclude anything: This if you tell me the animal in the bag is a mammal. Ok, so what? Yes, being a mammal is necessary for being a cat, but tons of animals are mammals. This doesn't let us make any valid conclusions about the animal in the bag. I have no fucking clue which mammal it could be. All I can say is "it's a mammal." But you already told me that.

Denying the necessary Lets Us Conclude Things: This is if you tell me the animal in the bag is NOT a mammal. Well, dang, now I know a lot! I know there's no fucking way it's a cat! (or a Carnivora, or a Felidae, and definitely not Felix!)

Affirming the Sufficient Lets Us Conclude Things: "The animal in the bag is definitely a cat." Whoa - I know a lot now! I know it's also a Felidae, Carnivora, and a Mammal! It HAS TO BE those things! (careful though - it doesn't tell us it's Felix!)

Denying the sufficient doesn't let us conclude anything: "That animal in the bag isn't a cat." Again, I can't conclude much of anything from this. It could still be a bunch of other things. You might already be starting to say something about Felix.

Hold that thought about Felix. We'll come back to it.

If you look at

felix --> cats --> felidae --> carnivora --> mammal

Consider that some things are sufficient to some parts, but necessary to others.

Let's say I have two animals in two bags.

One, i say, is a member of carnivora, the other, I say, is not a member of carnivora. What can I VALIDLY conclude about each animal?

think about it.

ok - let's check your thinking.

felix --> cats --> felidae --> carnivora --> mammal

Animal A, who I've affirmed membership in carnivora:

I can validly conclude that this animal is a mammal. I have no clue about anything to the left of that - is it a felidae, is it a cat, is it felix? No idea. This is because carnivora is SUFFICIENT for membership in mammals. However, it is NECESSARY to the rest of the stuff on the left. The only way I can work in that direction is with the contrapositive, which requires /carnivora (which isn't the case for this animal)

Animal B, who I've denied membership in carnivora:

Well - if it's not a carnivora, I know that it CAN'T be a member of the felidae family, I know it's not a cat, and I know it's not Felix the cat. These are all logically true statements. It could still be a mammal, though (or it could not!) I can't say anything one way or the other about that. Again - this is for the same reason. It is necessary to the stuff on the left, so denying it lets us conclude things on that side. It is sufficient to the stuff on the right, so saying "It's not a carnivora" doesn't tell us anything about if its a mammal.

Lastly: on the note of Felix.

You hopefully said that denying membership in Cats (again, remember house cats) earlier doesn't tell us anything about felidae (what if its a lynx or an ocelot), doesn't tell us anything about carnivora, doesn't tell us anything about being a mammal. Denying membership in cats, however, DOES tell us that this animal is not Felix.

OK - hopefully that helped.

The "cats and mammals" test is something I use every time I take a practice test, so I hope it helps you too.

now - for your example problem.

Cats -> mammals is a relationship.

The test will then sometimes give you an example to consider, ie, your example of "a speciment of plant x has blah blah blah". This is the animal in the bag.

for your example:

these are the relationships they've given us to work with:

fuzzy seeds-> long stems

fuzzy seeds -> /white flowers

curled -> white flowers

thorny seedpods -> curled leaves

given about our specimen (the animal in the bag):

x has a long stem and curled leaves

OK - we affirm long stems and curled leaves.

1. Fuzzy seeds -> long stems(we affirmed the necessary, and can't conclude

anything from this. If we tried to, we would be saying "all mammals are cats.)

2. Fuzzy seeds -> /white flowers (Can't conclude anything yet! We have nothing yet that could interact with this statement. Let's come back to if we learn more.)

3. Curled --> white flowers (We have affirmed the sufficient. the relationship says that if we have curled leaves, we MUST have white flowers. Our speciment does have curled leaves, so it must have white flowers. OK, We now know our mystery specimen has whiteflowers.)

Wait! We just learned we have white flowers! This might interact with our previous statement.

Let's go back to 2.

2A. fuzzy seeds -> /white flowers. Hmm.... If it's got fuzzy seeds, it must NOT have white flowers. We can also say "If it has white flowers, it must NOT have fuzzy seeds." (contrapositive)

2B. (Contrapositive) thus, white flowers --> /fuzzy seeds. AH hah! We can do something here! We know we have white flowers, we affirm the sufficient. We now KNOW our mystery plant does not have fuzzy seeds.

4:. thorny seedpods -> curled leaves

This is where you went wrong - you did an "All Mammals are Cats" here. We have affirmed the necessary - we know that our specimen has curled leaves. However, this relationship is only saying that curled leaves are necessary for something to have thorny seedpods. Thorny seed pods, on the other hand, are merely SUFFICIENT for having curled leaves.

There may be other ways to get curled leaves, just like the statement

cats -> mammals

leaves room for other ways to be a mammal other than being a cat (which we happen to also know is true from our general knowledge.) In short - affirming the necessary doesn't let us conclude anything.

OK - here's what we concluded.

We started with knowing that it has curled leaves and a long stem.

We concluded that our mystery specimen has white flowers, and it does not have fuzzy seeds.

There is an answer choice that perfectly matches:

"it has white flowers but lacks fuzzy seeds."

also: Take it from me, while you still have control, make sure you get a good GPA. That is your number one mission in undergrad. Don't be a splitter if you can help it. Focus on nailing classes the first time, because retakes are going to penalize you based on how LSAC does things.

Don't take practice LSATs yet.

Take conditional logic or get a book. also get exposure to reading academia both in science and humanities. Being able to read something complicated and have big picture understanding of it is huge. Read, read, read, and practice the skill of "What did I just read?" Low res and high res summaries.

Good luck, don't kill yourself practicing this stuff during undergrad, have fun and be a curious student of the world and you will do great.

E is tempting because of the similarity, but its saying "bucket a --M--> B (has photos),

bucket C ---M--> /B (does not have photos) , and so, Bucket A is bigger than Bucket C." It's so close, but its talking about the greater set, rather than the subset of the members who have photos (or have taken a particular class) that we are actually talking about. It can be sneaky when you're under time pressure, because both are definitely flaws for the same reason (we don't know how big either bucket is!), so it feels right.

you will never have a time in your life where you get a higher return on investment for each hour of studying than you will for the LSAT

if you already have a loving partner, great, but take this shit serious, get it done, and move forward with your life. you owe it to yourself because you want and deserve great things

I think this might go well at the beginning of the course, to be honest. Letting students know how the drilling tab works from their first 20 min with the platform, the importance of preserving later tests, etc. I think many students don't go through the whole thing before starting practice tests and drilling, and knowing this stuff up front would be helpful.