Open Q&A (Intermediate) with Mika

Hey, Raghu, good to see you again.

It's been a busy day around here, but should have a good night in front of me. See if more people show up this time.

think there's something wrong with the link last time.

Yeah. Well, we'll see. Fingers crossed. we actually, I don't know, get a couple more people. It's just good for me if it's an open Q&A, but I feel like we've been having a lot of open Q&A's this stretch and I feel like that's not healthy very much.

Yeah, yeah, so we'll just spend a one-on-one session again like last time if we end up not seeing anybody else.

Yeah, I get the inclination there.

So I would say one thing I do is I try to think about, why does the author care, right?

So instead of it being about whether I find it interesting, it's about me trying to sort of figure out why the author thinks that this is interesting and worth discussing.

So I think that's one way to approach it, just sort of a mindset shift from, I am trying to deduce what the author cares about.

I would say the other thing is, it's undoubtedly true that having an interest in the subject, being discussed is helpful, right?

just is. So I'm trying to, Kind of think about other than changing your mindset or focus on what you're thinking about.

Yeah, it's hard to tell. Oh, okay, we have more people trying. That's good. I'll think on that, Ragu, and if I have some further advice, I'll let you know.

Yeah. Blue. How's it going? All right. Well, any questions? It's just you guys right now. So anything you want to talk about or have me look at, just treat it like a mini tutoring session, I guess, at this point.

Okay. Well, what have I been working on that I'd love to talk about? Yeah, that's another good question to ask.

Yeah, I go for it right on.

Is that right? Yeah, the better you understand the argument. The usually, the clearer your anticipation of what the best answer will be.

I kind of forgot what you mentioned, though. OK, well, let's think about that. It definitely changes question type by question type.

But I always would say is you're not trying to come up with the perfect sentence, right? the perfect answer isn't going to be over there.

What you're trying to come up with is a concept of the answer, right? I need the answer to address this or to do this thing.

And then you look for an answer choice that achieves that purpose, right? So it's less about the specific wording and more about the idea as a whole.

I can definitely say with certain strategies, like on reading comp, if you know what framework you're in, that gives you a very clear idea of what the main point question needs, that what the answer to the main point question needs to be, right?

Because if I'm in an old new passage, then the main point is almost certainly going to mention the old and the new and maybe why there is a switch, right?

If I'm in a present debate, right, the main point question is absolutely going to describe the debate, some degree, and usually describe the author's resolution, if any, right?

Oh, in main point questions, you can and should always be striving to anticipate an answer, just based on what framework you've seen.

So that's why understanding the frameworks is quite important and can be quite helpful. It's not just a bunch of like technical mambo java we came up with for no reason, it has a lot of applicability.

There are certain questions for which anticipation is much harder, like most strongly supported. I would say on like one through three stars, you can still anticipate with very high likelihood of being correct.

But once you get to four and five star most strongly supported, they can come out at very weird angles, right?

Unexpected ideas that do in fact follow. And so inference type questions, like most strongly supported. Mainly most strongly supported is extremely hard to anticipate for it.

Necessary assumptions are also hard to drive anticipations once you get to the four and five-star level. They're similar in that way.

What else? Yeah, I think those are the two biggest deviations from anticipation. And then the other thing I would say is on sufficient assumptions and must be truths, it is possible to have a correct answer before you look at the answer choices, right?

You don't even really need to anticipate it because you can deduce it by using the conditional logic equations correctly.

so I would say those are the ones where you can have an absolute certainty about being right, whereas everything else, there's still a little bit of muckiness, right?

We have to anticipate rather than just be like, this is the answer. Yeah, all right. I know I went all over there, but I hope that was helpful.

That was perfect. you. All right, good. Any questions? Do I need to bust some stuff out on my own?

Oh, most strongly supported and necessary assumptions are, I think, the two hardest question types to anticipate answers for it.

Because both of them can go in very weird, unexpected directions while being absolutely correct. like, a strengthen, right, there's much narrow range of possible answer choices, I would say.

Yeah. Yeah. So, give me one second. Let's see about this. Well, I have been working on my conditional logic document a little bit.

As long as we're all here, I can bust that out and talk about some of the recent additions. So I'm pretty certain you both have access to this already, but if you don't, let's go ahead and drop that link into the chat.

So you've seen this before, you've definitely seen this page. So one of the things I am trying to emphasize more and more, or at least this is like a, you know, snappy term for it, but it's the rule of two in conditional logic, right?

When we look at a conditional logic statement, right, the fact that certain letters, certain variables show up twice is exactly what allows for the equation to work, right?

starting term to the first bridge term. First bridge term to the second bridge term, second bridge term to the end term, therefore starting term to end term, The rule of two, A has appeared twice, D has appeared twice, B and C have both appeared twice, right?

So for something to carry through in a four statements to be combinable, right, in conditional logic, they must share a term, right?

They have to have a shared term. That's what allows us to get from A to C. So when you're doing, for example, assumptions, right, you can always deduce at least which pieces need to which variables need to be in the answer based on counting, right?

If I see my start term twice and my B term twice, but I don't see my C term or my D and I only see my D term once, that tells me what's missing, right?

I just need to count, which ones haven't repeated, right? So you imagine this sufficient assumption question, right? B and C have not repeated.

A has and D has, and so what's missing has to be B to C, right? We can see it the other way, right?

A to D, I have D twice, I have C twice. A and B have not reappeared, and so the missing statement is A to B, right?

So simple rule of two. It needs to appear twice for it to have any function in a conditional logic argument.

Y'all may have seen this complex example before, but I'll also work through that because I'm enjoying teaching this one.

Also, this needs to be great, great next page, perfect. Actually, I kind of don't need that then. Anyways. So you guys may have seen this one.

I came up with this. It's not from a real question. I think this would be among the most complicated logical statements ever put on the LSAT if it were.

But I just want to run through a few things, which is once we have our rule of two in play, how do we match things up?

And the number one rule at this point is whenever I see a variable on the same side as itself, once positive and once negative, I need to take the contra positive.

Right? Because once I take the contra positive of E to negative B, that becomes B to negative D, and boom, suddenly we have our nice zigzag again, A to B, B to negative D.

Right? And then I just do the exact same thing again. Now I have negative D on the right side, but I have E to D or F up here.

Right? So negative D and D. here on the same side. So I take a second contrapositive, and that becomes not F and not D, lead to not E.

And from that, I can conclude that A and not F lead to not E. There we go. So any time you see a variable on the same size itself, once positive, once negative, take a contrapositive of one of those statements and restore this zigzag that we want to see.

OK, so that was some interesting stuff I came up with recently. And then I did this for a class a while ago, but it bears worth doing again.

I think it's really helpful. I did a class on what unconditional logic arguments are on the LSAT. And so this is what I came up with.

OK, the first thing I want to emphasize. is conditional statements versus a statement of existence, right? So we have a statement here, A to B, right?

This is a conditional, if A, then B. But then we have a statement that confirms A's existence, right? And if A leads to B and A exists, then we can conclude that B exists, right?

If I'm sleepy, I'll go to sleep. I am sleepy. Therefore, I will go to sleep, right? You will see this sort of set up on the LSAT and it's important to be able to distinguish between a statement of existence and a conditional statement, right?

So think of this as just a confirmation that one of the variables does, it can be backed, exists, right?

So, if we think about a few common ideas otherwise, right, we can have these sort of disjunctive requirements A or B.

If we have a statement that one exists, then we know that C exists, right? don't need B here. Then we have like a disjunctive requirement, right?

If A or B then C. B does not exist. Therefore, if A then C. You see how in the previous two, our conclusion was a statement of existence.

But here, our conclusion is conditional, right? we still don't know if A exists. We just know that B doesn't, right?

And so that leads us with a conditional conclusion rather than an existence conclusion. Yeah. Conjunctive requirements, right? We're saying that both exists.

Boom, we get our outcome. But you can also think of like, if we had a partial statement of existence, right?

Now we only said that A exists. And so our conclusion is that if B exists, then C exists, right?

So you can see because we didn't fulfill both requirements, our conclusion stays conditional. So again, I'll say they're doing this all over the exam.

It's important to recognize the difference when it happens because I've seen students tread water on questions that they would be able to fly through if only they would be more aware of this concept of a statement of existence.

Yeah. All right, we also have our standard template, if A to B, B to C, therefore, if A, C, right?

statement of existence is involved, so our conditional, our conclusion is fully conditional. But then you can imagine that we actually have a trigger for this.

If A, then B, if you then C, B, A exists, therefore, C exists for the Conjunction is it saying that if a then c This one up here The one right on top yeah conjunction in state of existence same enough existence, I'm Yeah, so this is where we're doing a joint statement of existence right and the both exist and therefore we can conclude that c exists Gotcha, so it's also a and b Oh, a s t and b s e right Say that again, sorry like is it saying I saw a lot of by my room is it saying each variable is also c like a s e and b s e?

No, no, so this is just confirming that a and b exists. Oh God, so this statement says if a and b exists then the c exists And then our second statement is confirming that a and b do exist

right okay so whenever you see the arrow that indicates that this is a conditional statement whereas this is a statement of existence right about reality not be yeah got you okay thank you no problem good question and then we have the standard template plus statement of existence right this is our normal setup except a is confirmed and therefore see exists you'll see a lot of oppositional statements so just remember what I said earlier right this is a constant contra positive right we wanted to take this not C to not B and we turn it into B to not C and then that makes our answer clear right you're gonna imagine an oppositional statement with statements of existence right so right now we know that if A then not C but we could also derive the contra positive if C then not A right and so here regard whichever direction we go

And we get not the other at the end. Inherited requirements start showing up a lot on four and five stars.

You saw one in that complex example I showed earlier. But so in this inherited requirement, right? A needs to be B and C lead to D, right?

Which means that we could also say that A and C lead to D, And so the C and C is an inherited requirement, right?

So we didn't confirm or deny C's existence. So we have to keep it with us as we move through the rest of the equation.

Then you can imagine, right, like a partial state of existence with an inherited requirement. So A leads to B, B and C lead to D, C exists.

And therefore, we can conclude that if a A exists. D would also exist. Yeah. All right. So C gets wiped out of the equation entirely.

A substitutes in for B and that gives us our conclusion. And then you have like a positive negative statement existence.

So you can compare that to where we have the B negative B over here. Now we have the A negative A over here, right?

Which again just means we need to take a contrapositive to get A on opposite sides. And I think that is all the stuff there.

There's been other stuff in here that I would like to talk about. No. No, nothing interesting. Yeah. All right.

Any questions that you guys came up with in the past minute?

For this stuff, um, so, reading often involves chains of causation, right? A is, A happens because B causes it, and B happens because C and B cause B.

So, there is somewhat, like, a similar thought process when you're dealing with long chains of causation in a reading cop passage, but that's really the only.

overlap, right? Conditional logic is a lot like it effectively is a type of math, right? And so it doesn't really mesh well with the reading comp framework.

I will say the idea of necessity and sufficiency still shows up, especially like in science and law passages, right?

the idea that something is required for something else to happen, or that something is sufficient to cause something else to happen.

So those concepts still still over, but this sort of like mathematical diagramming approach doesn't really translate at all. Yeah.

Thank you. Yeah. Well, yes, Zach. If nobody objects, we can always just make this like kind of like a quasi conditional logic day.

Let me get something set up. I will say one of the things I noticed recently when I was just working with a student is cannot be true questions seem to be coming back into Vogue.

So cannot be true questions were very common in like the early test like the first 20 or so. And then they sort of dropped out for a while, became less and less frequent and then they started picking up again a lot recently with like the most 10, like the 10 most recent tests.

So if you guys have questions about anything else, obviously like pause me or let me know and we can talk about that, otherwise let's you know, jump into some cannot be true questions.

Yeah, let me get this set up on the iPad. Okay, so sharing, yep, there we go. So you can see even like by how small I cannot be true packages, right?

It was gone for a while and now it's like kind of come back. Yeah, this doesn't have the high 80s or the 90s at all in it, those were a fair number.

But it's kind of interesting to think about it cannot be true, right? In reality, what we're doing is we're looking for a thing that has to be true and then we're looking for an answer that directly contradicts it, right?

So in a way, it cannot be true is just must be true, but instead of looking for an answer that says the thing that must be true, we're looking for an answer that denies the thing that must be true, right?

So like imagine I made just a random set of equations that were, oh, there we go. like A to B, B to C, to D, right?

Well, what do I know has to be true here? A to C has to be true, B to D has to be true, and A to D has to be true, right?

But it could be that C also leads to B, right? Nothing up here says that that's not allowable, right?

All we know so far is that B does lead to C. So that's possible, right? Is it also possible that D leads to B?

Well, nothing here contradicts that, right? What I'm looking for is something like A leads to Nazi, right? That would plainly contradict something that has to be true, right?

So would B leads to not B, that plainly contradicts something that must be true, and A leads to not D, plainly contradicting.

predict something that must be true. So that's the framework you should have when you run into a cannot be true question.

You are still looking for the things that must be true. Your analysis should be the exact same, except now you're looking for a statement that denies those things.

All right, so let's take a look at an intermediate question first. Let me clear that. Okay, let's check out this one first.

Just to warm up with like a, you know, a two star, three star. So to call on the statements, if true, provide a reason for rejecting which one of the following.

Some people argue that the government should not take over failing private sector banks because the government does not know how to manage financial

institutions. However, rather than managing a bank's day-to-day operations, the government would just need to select the bank's senior management.

Most politicians have yet never been military professionals, yet they appoint the top military officials entrusted with defending the country, at least as greater responsibility as managing a bank.

Okay, so this one doesn't necessarily feel like a true conditional logic argument, does it? We're not seeing a lot of repeated terms, right?

A to B, B to C, that rule of two. I'm not seeing enough to make that possible, right? So what I'm really looking at here is I think this combination here,

All right, let's take out the answers. A, planning a branch of military requires greater knowledge than running a bank.

Nothing up here denies that, right? The author says that it's as great or at least as great. So it could be greater, right?

We just know that it's at least as great. So A is possible. The author did not directly contradict it.

B, politicians do an adequate job of appointing the top military officials entrusted with defending the country. Nothing up here says that the government is doing a good job or not doing a good job, right?

It's just saying that they don't have to run these institutions directly because they can appoint people and military officials are an example of that.

So B, I think, also is possible. Nothing in the prompt rules it out. See, politicians are not capable of managing a bank's day-to-day operations.

Politicians are not capable of managing. I think the whole point up here is that they don't have to. Yeah.

So I don't think this is relevant. don't need to do this, right? The whole point up here is that they can hire people to do the day-to-day.

Nothing up here says that they're totally incapable, right? This says that some people argue this, but I don't think that that's a factual established, factually established.

I do think D makes sense here, right? The author's whole argument here is that it is possible for the government to manage financial institutions indirectly, right?

So I think the author, this columnist, would definitely 100% disagree with this statement. And then E, we never talked about financially sound, right?

They just talked about failing banks. So E is just like introducing a new concept entirely. So this one ended up being more like a most strongly supported cannot be true, right?

Which kind of makes sense, provide reason for rejecting, okay? Questions, thoughts? Right? Let's try an intermediate one. Okay, what's this one?

Okay, I love this question. This is a quasi-logic gain question. And quite fun for that reason since logic games, obviously no longer exists.

So, let's just check this out. Among the small to medium sized marine animals, as seals and dolphins, the longer an animal can stay submerged, the greater the depth the animal can reach.

Dolphins can go to greater depths than northern fur seals, and elephant seals can stay submerged longer than the wettled seals.

So, let's just remember the relationship. The longer you can stay submerged, the greater the depth you can reach. So, those two are treated as basically co-occurring.

So, what I see here is that we basically have dolphins before northern fur seals, and we also have elephant seals before wettled seals.

Great. Currently, there is no direct relationship between these sets, right? We just know the relationship between dolphins and spurs eels and between elephants and wettles.

So our answer choices, obviously, are playing with these relationships, right? So what are we looking for, right? We're looking for something that creates a circle, basically, right, dolphins are somehow, I guess, maybe behind northern fur seals, with wettles seals, and e, is that right?

Yeah, right, some sort of impossible circular relationship, where d is maybe faster than e, but somehow also slower than ws, right?

That would be impossible. So, let's just walk through, we're just going to kind of test that idea out, like, is this a possible alignment?

Dolphins are deeper than Weddle seals, but not the same depth as elephants, so that would basically say elephants, dolphins, leto seals.

That's fine, right? We can put dolphins in between these two. There's nothing contradictory here. Weddle seals can stay submerged longer than northern fur seals, but dolphins can go deeper than Weddle seals.

So this is similar right now. Instead, we just have W-S-N-F-S. Again, there's no contradiction here, right? Perfectly possible. Weddle seals can dive to greater depths than dolphins and can stay submerged longer than northern fur seals can.

So tempting, but this one I think is basically saying, Weddle seals are before both of them, right? therefore Weddle seals are before dolphins and dolphins are still before NFS.

So, that doesn't seem to be a problem. First seals can stay longer than elephants. But wettlesseals can go further than dolphins.

And boom, now we have the contradiction. Dolphins need to be in front of northern first seals, but they're also behind wettlesseals.

And that is impossible, right? So, D is the correct answer here. All right. Should I give you all time to try out the next one on your own?

Let's do that. Unless you guys have questions or anything you'd like to move over to. Okay. Okay. Hey, so a lot of the cannot be trues or phrase just as this could be true except, right?

That means the same thing as cannot be true. Okay, let's take like five minutes, come back to 540 and then we'll talk about it.

You You Okay, blue slide and A. Let's take another one here. Give it like one more minute. I will say I don't think it's A.

Don't think it's A. I know it's tempting because then it's like, why is this so? Sociologists even bothering to talk about this, right?

It's like one of those, like, easy inferences, but with the LSAT, right? we need them to specifically say it.

Yeah. So it could be that the sociologist is talking about a problem that doesn't even exist. I think that's kind of dumb, but I think that's what the LSAT would have treated as.

Yeah. Great. So let's just walk through it. Um, B seems possible. They talk about demagogues specifically doing this, but they don't

ever say that only demagogues do this. So B makes sense. It's perfectly possible other people try to exploit reality.

We never really talked about this idea of highly emotional versus less emotional people. So this is possible, right? We literally don't have anything that talks about it.

But I do think B is the answer here, right? Critical thinking is the only adequate protection. And so this says that the mere presence of an early system of government provides adequate protection.

I think that would contradict the only statement here. Yeah. So that's why I would choose D in this instance.

And then E. We didn't talk about electronic media like it's presence. And in fact, This isn't about erosion of media freedoms, right?

It's about protection against demagogues, so E is again kind of veering off into a topic we didn't talk about, and therefore it's possible it could be true, because we just didn't talk about it at all.

Yeah. That makes sense. Yeah, you definitely, with these cannot be truths, you definitely want to be looking for only statements both down here and up here, because that is often a good way for them to generate something that cannot be true, right?

apply in only somewhere else. Sorry, I had to spray a cat that was stealing food. Um, Let's try another.

Take a look at this one. Come back in like four or five minutes. Cool, it's gonna be four minutes, whenever you're ready.

I'll show you about some things you love. You You You All right, let's talk about it. So, as I may have indicated.

and the text with blue, and the text chat with blue. I do think the answer choice is D, right?

What can be rejected? So they clearly do have a way of telling names and species, right? And they're now figuring out that many of the names, wait a minute, species have been given distinct names, actually blood.

Yes, right, they couldn't be able to determine this information without being able to determine this. So again, it's like, what can we reject with C?

I don't think we know, right? We do know that botany has this problem, but we don't know about other fields.

This, they don't talk about whether this will help botanists or hurt them in any way, so we just don't know.

A, most of the duplicates and omissions have yet to be cleared up. We don't know the volume, right? percentage of them are going wrong.

So A is out, and E, a person who consults the scientific record, looking under only one of the plant's names, may miss available information about that plant.

I think this is absolutely true, right? They're specifically saying that this is a possibility, right? We have long, we have varieties that are thought to be the same species that are actually different species, and we know that they've been naming them that were already named.

So I think E, sorry, E is something that has to be true as opposed to the one that cannot be true.

Yeah. So the question here is, which one of these claims cannot possibly be true? And I don't think we know enough

about fields other than botany to say whether or not there are duplicates and omissions in the record, right? We only know about botany.

So I don't think we can disprove C. Does that make sense? Awesome. All right. Let's try one advanced one.

Yeah, and then we'll probably call it a day after that. That was my little demonstration before. Okay. So here is definitely a very conditional logic-y one.

So keep that in mind. Yeah, take five minutes, come back at 555 and talk about it. Oh, I didn't Alright, well, let's finish this last one off then.

So, to be kind, one must want that person to prosper. So, if kind, prosper. Um, may never the less is a bit weird, I'm going to skip past.

asked it for now. No two people who dislike each other can be fully content. So if dislike, then not fully content.

And any two people who do not dislike each other will be kind to each other. So what can we come up with here?

Well, let's just rephrase a couple of things, right? So first off, I'm seeing kind on two ends, right? So I want to combine these statements.

So if not dislike, then kind. If kind, then prosper, right? And that lets me clearly get to the idea that if you don't dislike each other, then you must want each other to prosper, right?

Okay. Okay, I am also seeing these two on the same side as each other, right, which means I can take the contra positive of one and get another functional statement.

And so if I do that, I think I get not kind leads to dislike. And then I get dislike leads to not fully content.

So therefore, if you are not kind to another person, then you will not be fully content and their presence.

Okay, so I am looking for something that would directly contradict either of these, right? So let's see, I either want something that says like two people that don't dislike each other, also don't want each other to prosper, or something like somebody who is not kind to another person can still be fully content and they're present.

So let's see. Some people who like each other are not fully content. I don't think we know that, right?

We know that if you dislike someone, you won't be fully content. I don't think we know anything about what happens if you do like someone, right?

We can definitely say that if you're fully content, then you must like someone. But again, I think A is still possible.

It's not ruled out. Some people who are fully content do not want each other to prosper. Now, that's interesting, right?

Because what I have here is, if you're not fully, if you're not kind, you won't be fully content. So if I take that, fully content leads to kind, right?

And we take this statement, right? Kind leads to prosper. And therefore, if you're fully content, you must want somebody to cross her.

Ooh, so I think that is, in fact, our answer, B doesn't seem possible. would contradict this. Some people who treat each other with respect are not fully content.

No, this is a misleading sentence, right? May nevertheless, that's not usable, right? If-then statements are if-then, they're not permissive.

Maybe, if-then, maybe, that doesn't work for conditional logic. D, some people who want each other to prosper dislike each other.

Here, we know that if you don't dislike each other, you must want the other person to prosper. But again, I don't think what we-we know what happens if you dislike somebody other than you won't be fully content.

Yeah. So, D is out, and E, some people who are kind do not treat each other with respect. And we can't use that sentence for anything just because of the way it's raised.

So that's out and the answer choice is B. Yeah, there we go. All right. Any final questions before we call it a day?

All right. Well, thanks for I think when will I be back next week? I will be back next week with parallel reasoning, I think.

Yeah.