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If you prepare for the LSAT, you will do well on it. Well, that's true. I can tell you that. But what if you go there and just by sheer luck, you fill out random bubbles on the LSAT, and you get a 180? I mean, look, it's not going to happen. But it could happen. | Understanding LSAT Logic_segment1.mp3 |
But what if you go there and just by sheer luck, you fill out random bubbles on the LSAT, and you get a 180? I mean, look, it's not going to happen. But it could happen. It's possible. And that demonstrates that these sufficient conditions are not necessary. We don't need you to prepare in order to do well. | Understanding LSAT Logic_segment1.mp3 |
It's possible. And that demonstrates that these sufficient conditions are not necessary. We don't need you to prepare in order to do well. Trust me, it's a way better idea than going in there and filling out random bubbles. But technically speaking, you don't need to prepare to do well. You either have to prepare or be extremely lucky. | Understanding LSAT Logic_segment1.mp3 |
Trust me, it's a way better idea than going in there and filling out random bubbles. But technically speaking, you don't need to prepare to do well. You either have to prepare or be extremely lucky. So the choice is yours. Let's compare if-then conditionals to conditionals that use only. Where if-then conditionals presented sufficient conditions, conditionals that use only present the necessary conditions, but actually not sufficient conditions. | Understanding LSAT Logic_segment1.mp3 |
So the choice is yours. Let's compare if-then conditionals to conditionals that use only. Where if-then conditionals presented sufficient conditions, conditionals that use only present the necessary conditions, but actually not sufficient conditions. So take a look at these. I will attend only if I can afford it. This is the necessary condition for my attendance. | Understanding LSAT Logic_segment1.mp3 |
So take a look at these. I will attend only if I can afford it. This is the necessary condition for my attendance. I have to be able to afford whatever this event is in order to attend it. If that condition isn't met, I'm not going to be there. It's a necessary condition. | Understanding LSAT Logic_segment1.mp3 |
I have to be able to afford whatever this event is in order to attend it. If that condition isn't met, I'm not going to be there. It's a necessary condition. But it's not sufficient. Even if I can't afford it, I might not go. It's kind of tricky. | Understanding LSAT Logic_segment1.mp3 |
But it's not sufficient. Even if I can't afford it, I might not go. It's kind of tricky. You look at it here. It might seem to you upon reading this naturally that this is a sufficient condition, that I will attend if I can afford it. But that's not what this says. | Understanding LSAT Logic_segment1.mp3 |
You look at it here. It might seem to you upon reading this naturally that this is a sufficient condition, that I will attend if I can afford it. But that's not what this says. It doesn't say I will attend if I can afford it. It says I will attend only if I can afford it. And on the LSA, you need to understand that statement as presenting a necessary but not sufficient condition. | Understanding LSAT Logic_segment1.mp3 |
It doesn't say I will attend if I can afford it. It says I will attend only if I can afford it. And on the LSA, you need to understand that statement as presenting a necessary but not sufficient condition. Let's take a look at a second one. Only if enough heat is applied to it does water boil. Okay. | Understanding LSAT Logic_segment1.mp3 |
Let's take a look at a second one. Only if enough heat is applied to it does water boil. Okay. Where is the necessary condition in this one? Well, it's right here. The necessary condition for water boiling is that enough heat is applied to it. | Understanding LSAT Logic_segment1.mp3 |
Where is the necessary condition in this one? Well, it's right here. The necessary condition for water boiling is that enough heat is applied to it. You need this to happen. Water cannot boil unless this necessary condition is in force. It's important that you see the difference between conditionals that say if then and conditionals that use only. | Understanding LSAT Logic_segment1.mp3 |
You need this to happen. Water cannot boil unless this necessary condition is in force. It's important that you see the difference between conditionals that say if then and conditionals that use only. If then conditionals present sufficient conditions but not necessary ones. There are other ways of achieving the outcome. And conditionals with only present necessary conditions but conditions that are not sufficient. | Understanding LSAT Logic_segment1.mp3 |
If then conditionals present sufficient conditions but not necessary ones. There are other ways of achieving the outcome. And conditionals with only present necessary conditions but conditions that are not sufficient. So we need these things to happen but they're not enough. Some other things might also need to happen. Okay, but what if we combine them? | Understanding LSAT Logic_segment1.mp3 |
So we need these things to happen but they're not enough. Some other things might also need to happen. Okay, but what if we combine them? Conditionals that have if and only if. What do you figure is going on there? Sufficient, necessary. | Understanding LSAT Logic_segment1.mp3 |
Conditionals that have if and only if. What do you figure is going on there? Sufficient, necessary. Think about it for a second. I hope you guessed it. Necessary and sufficient. | Understanding LSAT Logic_segment1.mp3 |
Think about it for a second. I hope you guessed it. Necessary and sufficient. Okay, so a person is eligible if and only if she lives in this country. It's pretty straightforward really. Just kind of take them one at a time. | Understanding LSAT Logic_segment1.mp3 |
Okay, so a person is eligible if and only if she lives in this country. It's pretty straightforward really. Just kind of take them one at a time. Get rid of this only if for a second. A person is eligible if she lives in this country. So being in this country is sufficient for eligibility. | Understanding LSAT Logic_segment1.mp3 |
Get rid of this only if for a second. A person is eligible if she lives in this country. So being in this country is sufficient for eligibility. But as that stands we'd say but it's not necessary. But we have this here. And only if. | Understanding LSAT Logic_segment1.mp3 |
But as that stands we'd say but it's not necessary. But we have this here. And only if. That adds the necessary condition. So living in this country is enough and it's necessary for a person to be eligible. Again, a number is prime if and only if it is only divisible by one and itself. | Understanding LSAT Logic_segment1.mp3 |
That adds the necessary condition. So living in this country is enough and it's necessary for a person to be eligible. Again, a number is prime if and only if it is only divisible by one and itself. This rule about divisibility is enough to define a number as prime. And it's necessary. It's the only way a number can be prime. | Understanding LSAT Logic_segment1.mp3 |
This rule about divisibility is enough to define a number as prime. And it's necessary. It's the only way a number can be prime. Necessary and sufficient. Alright, moving right along. There are times in the LSAT when you're going to want to be able to use symbolic logic. | Understanding LSAT Logic_segment1.mp3 |
Necessary and sufficient. Alright, moving right along. There are times in the LSAT when you're going to want to be able to use symbolic logic. Which is pretty much what it sounds like. It is something that enables you to reduce large chunks of text into symbols. And then to represent the logical structure in that paragraph or that blurb with the symbols. | Understanding LSAT Logic_segment1.mp3 |
Which is pretty much what it sounds like. It is something that enables you to reduce large chunks of text into symbols. And then to represent the logical structure in that paragraph or that blurb with the symbols. So you're going to have from big blocks of text you're going to reduce that to just letters and arrows. Where the letters represent certain statements or clauses and the arrows represent the logical structure. It will be a lot clearer if I show you. | Understanding LSAT Logic_segment1.mp3 |
So you're going to have from big blocks of text you're going to reduce that to just letters and arrows. Where the letters represent certain statements or clauses and the arrows represent the logical structure. It will be a lot clearer if I show you. So let's go ahead and revisit a little argument that we dealt with earlier in the lesson about poor Tom who is going to be heartbroken because of Erica. And let's go ahead and reduce this to symbols. Using just letters and arrows. | Understanding LSAT Logic_segment1.mp3 |
So let's go ahead and revisit a little argument that we dealt with earlier in the lesson about poor Tom who is going to be heartbroken because of Erica. And let's go ahead and reduce this to symbols. Using just letters and arrows. So let's start at the beginning. Tom is going to be heartbroken tomorrow. I'm going to try to choose something from this clause here. | Understanding LSAT Logic_segment1.mp3 |
So let's start at the beginning. Tom is going to be heartbroken tomorrow. I'm going to try to choose something from this clause here. It's actually a whole sentence. But I'm going to try to choose something from here that kind of makes it stick out from the other sentences. I'm not going to use Tom here. | Understanding LSAT Logic_segment1.mp3 |
It's actually a whole sentence. But I'm going to try to choose something from here that kind of makes it stick out from the other sentences. I'm not going to use Tom here. I don't want to use T for Tom because Tom is in some of the other bits. But heartbroken is its own thing. So I'm going to actually represent this whole bit here. | Understanding LSAT Logic_segment1.mp3 |
I don't want to use T for Tom because Tom is in some of the other bits. But heartbroken is its own thing. So I'm going to actually represent this whole bit here. Tom is going to be heartbroken tomorrow. As H. H stands for Tom is going to be heartbroken tomorrow. Alright, next bit. | Understanding LSAT Logic_segment1.mp3 |
Tom is going to be heartbroken tomorrow. As H. H stands for Tom is going to be heartbroken tomorrow. Alright, next bit. If Tom asks Erica out, she will definitely say no. And if Erica says no, Tom will be immediately heartbroken. Now it's not just about sentences. | Understanding LSAT Logic_segment1.mp3 |
If Tom asks Erica out, she will definitely say no. And if Erica says no, Tom will be immediately heartbroken. Now it's not just about sentences. It's about the logical chunks. Hopefully this kind of sticks out to you now or this makes sense to you now having gone through most of this lesson. But I'm actually going to represent each of the logical chunks as a symbol. | Understanding LSAT Logic_segment1.mp3 |
It's about the logical chunks. Hopefully this kind of sticks out to you now or this makes sense to you now having gone through most of this lesson. But I'm actually going to represent each of the logical chunks as a symbol. So for this one I'm going to use A for asks. So this represents Tom asks Erica out. Next one. | Understanding LSAT Logic_segment1.mp3 |
So for this one I'm going to use A for asks. So this represents Tom asks Erica out. Next one. She will definitely say no. I'm going to refer to that as N. If Erica says no, that's the same thing. Saying no. | Understanding LSAT Logic_segment1.mp3 |
Tom plans to ask Erica out tomorrow, that's A again. Now this will all be clear once you see it all come together with the arrows. Now let's remember the logical structure and let's go ahead and write this in symbolic logic form. The first part of the logical structure was if Tom asks Erica out, she will definitely say no. So I'm going to represent that as asks out, then, no. Okay, and what this here says, if he asks her out, then she'll say no. | Understanding LSAT Logic_segment2.mp3 |
The first part of the logical structure was if Tom asks Erica out, she will definitely say no. So I'm going to represent that as asks out, then, no. Okay, and what this here says, if he asks her out, then she'll say no. And I'm going to actually combine the next part which would be, it would be something like, if Erica says no, then Tom will be heartbroken. That's the next part logically, but I'm not going to put it here. I'm just going to go ahead and throw that right on here, because it follows logically. | Understanding LSAT Logic_segment2.mp3 |
And I'm going to actually combine the next part which would be, it would be something like, if Erica says no, then Tom will be heartbroken. That's the next part logically, but I'm not going to put it here. I'm just going to go ahead and throw that right on here, because it follows logically. So, so far we have, if Tom asks Erica out, she will say no. If she says no, then he'll be heartbroken. And what this here does, Tom plans to ask Erica out tomorrow, that just tells us that yes, A is happening. | Understanding LSAT Logic_segment2.mp3 |
So, so far we have, if Tom asks Erica out, she will say no. If she says no, then he'll be heartbroken. And what this here does, Tom plans to ask Erica out tomorrow, that just tells us that yes, A is happening. A occurs. It tells us to kind of start this chain going. And now, look at just this right here. | Understanding LSAT Logic_segment2.mp3 |
A occurs. It tells us to kind of start this chain going. And now, look at just this right here. If you didn't even have these words, and all you had was this little chain, and the knowledge that yes, A is in effect, you could very easily get here without having to go back and work through all the details. I tell you if A, then N, and consequently, then H. And then I tell you yes, A. A is going on. | Understanding LSAT Logic_segment2.mp3 |
If you didn't even have these words, and all you had was this little chain, and the knowledge that yes, A is in effect, you could very easily get here without having to go back and work through all the details. I tell you if A, then N, and consequently, then H. And then I tell you yes, A. A is going on. Start the chain. So you say A is going on, okay, we're good to go. That means I can get all the way to H. So from A, I can conclude H. Okay, I know that was a lot. | Understanding LSAT Logic_segment2.mp3 |
Start the chain. So you say A is going on, okay, we're good to go. That means I can get all the way to H. So from A, I can conclude H. Okay, I know that was a lot. I know it was fast. But don't worry, we're going to have plenty of more opportunities for practice. This time, I'm going to have you try it. | Understanding LSAT Logic_segment2.mp3 |
I know it was fast. But don't worry, we're going to have plenty of more opportunities for practice. This time, I'm going to have you try it. This blurb is a little bit more straightforward than the other one. So we'll take a step back, make it a little bit easier. The textual sequence here mirrors the logical sequence. | Understanding LSAT Logic_segment2.mp3 |
This blurb is a little bit more straightforward than the other one. So we'll take a step back, make it a little bit easier. The textual sequence here mirrors the logical sequence. So you don't have to kind of like figure out where everything goes. It's just straightforward, logical sequence and textual sequence are the same. The only thing that is a little tricky about this, and it's not that tricky, it just requires a little bit of instruction, is that when a statement says not, right, and it's here, the mayor will not make his big speech. | Understanding LSAT Logic_segment2.mp3 |
So you don't have to kind of like figure out where everything goes. It's just straightforward, logical sequence and textual sequence are the same. The only thing that is a little tricky about this, and it's not that tricky, it just requires a little bit of instruction, is that when a statement says not, right, and it's here, the mayor will not make his big speech. I want you to represent that not separately from the letters and the arrows. So let's take a random example. If the sentence was, the birds will not fly south for the winter. | Understanding LSAT Logic_segment2.mp3 |
I want you to represent that not separately from the letters and the arrows. So let's take a random example. If the sentence was, the birds will not fly south for the winter. I don't want you to represent that as F for will not fly south for the winter. What I want you to do instead is have F stand for the birds will fly south for the winter. And I want you to put this symbol in front of it. | Understanding LSAT Logic_segment2.mp3 |
I don't want you to represent that as F for will not fly south for the winter. What I want you to do instead is have F stand for the birds will fly south for the winter. And I want you to put this symbol in front of it. It's a negation symbol. So this means not F. Don't worry, we'll go over this in some practice sessions in a little bit. But you're going to have to use this negation symbol when you translate this blurb into its symbolic form. | Understanding LSAT Logic_segment2.mp3 |
It's a negation symbol. So this means not F. Don't worry, we'll go over this in some practice sessions in a little bit. But you're going to have to use this negation symbol when you translate this blurb into its symbolic form. So just remember that. I'll go ahead and pause the video now. And you take out a piece of paper. | Understanding LSAT Logic_segment2.mp3 |
So just remember that. I'll go ahead and pause the video now. And you take out a piece of paper. You don't want to just do this in your head. Take out a piece of paper and a pen or pencil and take a look at this blurb, write down the symbolic form of it by giving each logical chunk a letter and then using arrows to represent the logical relation between the symbols. Alright, let's take it slowly and we'll take it in turn. | Understanding LSAT Logic_segment2.mp3 |
You don't want to just do this in your head. Take out a piece of paper and a pen or pencil and take a look at this blurb, write down the symbolic form of it by giving each logical chunk a letter and then using arrows to represent the logical relation between the symbols. Alright, let's take it slowly and we'll take it in turn. Remember, each logical chunk is going to get its own symbol. Let's start with the first one. If it rains in Philadelphia. | Understanding LSAT Logic_segment2.mp3 |
Remember, each logical chunk is going to get its own symbol. Let's start with the first one. If it rains in Philadelphia. I'm not going to use P here because we have the parade involved. I think it would be easier if we just use R for rain. So this R means it rains in Philadelphia. | Understanding LSAT Logic_segment2.mp3 |
I'm not going to use P here because we have the parade involved. I think it would be easier if we just use R for rain. So this R means it rains in Philadelphia. The next chunk, the parade will be cancelled. I'm going to say that is C for cancelled. If the parade is cancelled, that's the same thing. | Understanding LSAT Logic_segment2.mp3 |
The next chunk, the parade will be cancelled. I'm going to say that is C for cancelled. If the parade is cancelled, that's the same thing. Cancelled. The mayor will not, remember not, not make his big speech. So I'm going to have S mean the mayor will make his big speech and I'm going to negate it. | Understanding LSAT Logic_segment2.mp3 |
Cancelled. The mayor will not, remember not, not make his big speech. So I'm going to have S mean the mayor will make his big speech and I'm going to negate it. It's not the case that the mayor will make his big speech. And if the mayor does not make his big speech, okay, if not S, he will not be re-elected. Okay, another not. | Understanding LSAT Logic_segment2.mp3 |
It's not the case that the mayor will make his big speech. And if the mayor does not make his big speech, okay, if not S, he will not be re-elected. Okay, another not. So we already have an R, so I can't use re-elected, so I'll use E, it's close enough. E is for re-elected and it's a not. Okay, now let's put this in order. | Understanding LSAT Logic_segment2.mp3 |
So we already have an R, so I can't use re-elected, so I'll use E, it's close enough. E is for re-elected and it's a not. Okay, now let's put this in order. If it rains in Philadelphia, the parade will be cancelled. Okay, that's R and then C. If R, then C. If C, then not S. Okay, so I can keep the chain going. C, then not S. And if not S, then not E. Okay, so what that tells us is actually, if it rains in Philadelphia, the mayor will not be re-elected. | Understanding LSAT Logic_segment2.mp3 |
If it rains in Philadelphia, the parade will be cancelled. Okay, that's R and then C. If R, then C. If C, then not S. Okay, so I can keep the chain going. C, then not S. And if not S, then not E. Okay, so what that tells us is actually, if it rains in Philadelphia, the mayor will not be re-elected. Right, it shows us the whole logical chain. And it does it in far fewer letters than it's done in the paragraph. Right, look how much shorter and easier to digest this is here than this whole thing here. | Understanding LSAT Logic_segment2.mp3 |
Right, it shows us the whole logical chain. And it does it in far fewer letters than it's done in the paragraph. Right, look how much shorter and easier to digest this is here than this whole thing here. And yeah, it's a little confusing at first, understanding which bits get their own symbols. Should I use not? Of course, when to use not? | Understanding LSAT Logic_segment2.mp3 |
And yeah, it's a little confusing at first, understanding which bits get their own symbols. Should I use not? Of course, when to use not? And linking the various conditionals together. But this is a skill you're going to practice. And it's become second nature to you. | Understanding LSAT Logic_segment2.mp3 |
And linking the various conditionals together. But this is a skill you're going to practice. And it's become second nature to you. And then you're going to be able to take certain arguments. Not all of them are great candidates. You're not going to do this even most of the time. | Understanding LSAT Logic_segment2.mp3 |
And then you're going to be able to take certain arguments. Not all of them are great candidates. You're not going to do this even most of the time. But there are certain times, certain arguments, and all the time, pretty much in the logic game sections. That's the analytical reasoning section. But those certain times, you're going to want to use symbolic logic to boil things down to a simpler symbolic form. | Understanding LSAT Logic_segment2.mp3 |
But there are certain times, certain arguments, and all the time, pretty much in the logic game sections. That's the analytical reasoning section. But those certain times, you're going to want to use symbolic logic to boil things down to a simpler symbolic form. Let's try another one, and this time, introduce a couple of new elements. So now we're going to talk about conjunctions and disjunctions, which are just fancy names for statements that use and, that's conjunctions, and statements that use or, those are disjunctions. And we're going to put in new symbols for each of these kinds of statements, right? | Understanding LSAT Logic_segment2.mp3 |
Let's try another one, and this time, introduce a couple of new elements. So now we're going to talk about conjunctions and disjunctions, which are just fancy names for statements that use and, that's conjunctions, and statements that use or, those are disjunctions. And we're going to put in new symbols for each of these kinds of statements, right? So when we see and, we're going to use this statement, kind of looks like an A. And when we see or, we're going to use this statement, which doesn't look like an O or an or or anything. But it is the disjunction statement. | Understanding LSAT Logic_segment2.mp3 |
So when we see and, we're going to use this statement, kind of looks like an A. And when we see or, we're going to use this statement, which doesn't look like an O or an or or anything. But it is the disjunction statement. So let's now take these new elements and add them to what we've already got, and try to reduce this little blurb here into symbolic form. If it is a sunny day, and he has enough time, Sam will walk to school. Alright, let's make, if it's a sunny day, sunny day is S, and, and I'm not going to put the conjunction or disjunction bits here, that's only when we actually write down the symbolic form down here. | Understanding LSAT Logic_segment2.mp3 |
So let's now take these new elements and add them to what we've already got, and try to reduce this little blurb here into symbolic form. If it is a sunny day, and he has enough time, Sam will walk to school. Alright, let's make, if it's a sunny day, sunny day is S, and, and I'm not going to put the conjunction or disjunction bits here, that's only when we actually write down the symbolic form down here. But for now we're just doing logical chunks. It's a sunny day, S, he has enough time, let's make that T, Sam will walk to school, let's make that W, if he walks to school, that's the W again, he will either walk, he'll walk with either Bart or Alex. Okay, let's just give them the, the letters for their names. | Understanding LSAT Logic_segment2.mp3 |
But for now we're just doing logical chunks. It's a sunny day, S, he has enough time, let's make that T, Sam will walk to school, let's make that W, if he walks to school, that's the W again, he will either walk, he'll walk with either Bart or Alex. Okay, let's just give them the, the letters for their names. And let's go ahead and put this into symbolic form. Okay, if it's a sunny day, and he has enough time, then, right, the implied, then, Sam will walk to school. If he walks to school, then, he'll walk with either Bart, or, Alex. | Understanding LSAT Logic_segment2.mp3 |
And let's go ahead and put this into symbolic form. Okay, if it's a sunny day, and he has enough time, then, right, the implied, then, Sam will walk to school. If he walks to school, then, he'll walk with either Bart, or, Alex. Okay, there we have it. If S and T, then W, and if W, then B or A. If it's a sunny day, and he has enough time, then Sam will walk, if he walks, it will be with either Bart or Alex. | Understanding LSAT Logic_segment2.mp3 |
Okay, there we have it. If S and T, then W, and if W, then B or A. If it's a sunny day, and he has enough time, then Sam will walk, if he walks, it will be with either Bart or Alex. Okay, one more thing, and then I promise we are going to get to some practice. But first we have to talk about contrapositives. Those contrapositives are pretty cool, actually. | Understanding LSAT Logic_segment2.mp3 |
Okay, one more thing, and then I promise we are going to get to some practice. But first we have to talk about contrapositives. Those contrapositives are pretty cool, actually. This is really where logic starts to work for you. And I mean, I guess it's been working for us the whole time, making things easier to follow, helping us to understand the logical structure of things. But here is where we can actually learn more than what is written on the page, as long as we understand the underlying logical structure. | Understanding LSAT Logic_segment2.mp3 |
This is really where logic starts to work for you. And I mean, I guess it's been working for us the whole time, making things easier to follow, helping us to understand the logical structure of things. But here is where we can actually learn more than what is written on the page, as long as we understand the underlying logical structure. Okay, so let's take a look at this one here. If it is snowing, Jamal is happy. Okay, pretty simple stuff, right? | Understanding LSAT Logic_segment2.mp3 |
Okay, so let's take a look at this one here. If it is snowing, Jamal is happy. Okay, pretty simple stuff, right? This is a sufficient condition for Jamal to be happy. We know this is a circumstance, the snow, this is a circumstance that guarantees this result. If it is snowing, then we know Jamal is happy. | Understanding LSAT Logic_segment2.mp3 |
This is a sufficient condition for Jamal to be happy. We know this is a circumstance, the snow, this is a circumstance that guarantees this result. If it is snowing, then we know Jamal is happy. Now can you take anything else from this statement? Is there anything extra that you can learn from this statement? What if I told you that Jamal is not happy right now? | Understanding LSAT Logic_segment2.mp3 |
Now can you take anything else from this statement? Is there anything extra that you can learn from this statement? What if I told you that Jamal is not happy right now? How about then? Could you find anything new from this statement? I hope you guessed it. | Understanding LSAT Logic_segment2.mp3 |
How about then? Could you find anything new from this statement? I hope you guessed it. We would know that it's not snowing, because this is sufficient to guarantee this result. If this result isn't happening, we know that this isn't happening either, because this automatically leads to this. So let's write this out in symbolic form. | Understanding LSAT Logic_segment2.mp3 |
We would know that it's not snowing, because this is sufficient to guarantee this result. If this result isn't happening, we know that this isn't happening either, because this automatically leads to this. So let's write this out in symbolic form. Let's have S for snowing, and H for happy. This will say, if it is snowing, then Jamal is happy. Now what we know, the new bit that we know, and this is the contrapositive, if Jamal is not happy, we are guaranteed to know that it's not snowing. | Understanding LSAT Logic_segment2.mp3 |
Let's have S for snowing, and H for happy. This will say, if it is snowing, then Jamal is happy. Now what we know, the new bit that we know, and this is the contrapositive, if Jamal is not happy, we are guaranteed to know that it's not snowing. Because the snowing would automatically trigger Jamal being happy. This second bit is the contrapositive of this statement here. If Jamal is not happy, then it's not snowing, and the snowing is the contrapositive of if it's snowing, Jamal is happy. | Understanding LSAT Logic_segment2.mp3 |
Because the snowing would automatically trigger Jamal being happy. This second bit is the contrapositive of this statement here. If Jamal is not happy, then it's not snowing, and the snowing is the contrapositive of if it's snowing, Jamal is happy. That's new information. That tells us something about a new situation that's not even dealt with over here. It tells us about the situation where Jamal is not happy. | Understanding LSAT Logic_segment2.mp3 |
That's new information. That tells us something about a new situation that's not even dealt with over here. It tells us about the situation where Jamal is not happy. So if we know for some reason or another that Jamal is not happy, we know something else about the weather. That's new information because we understand the underlying logical structure, and we know what a contrapositive is. So how did I get this? | Understanding LSAT Logic_segment2.mp3 |
So if we know for some reason or another that Jamal is not happy, we know something else about the weather. That's new information because we understand the underlying logical structure, and we know what a contrapositive is. So how did I get this? I used the formula here. You negate what's on the right side of the arrow, and bring it on over to the left. You negate what's on the left side of the arrow, and you bring it on over to the right. | Understanding LSAT Logic_segment2.mp3 |
I used the formula here. You negate what's on the right side of the arrow, and bring it on over to the left. You negate what's on the left side of the arrow, and you bring it on over to the right. So here it was happy, move it on over, not happy. Here it was snowing, move it on over, not snowing. That is how you get the contrapositive. | Understanding LSAT Logic_segment2.mp3 |
So here it was happy, move it on over, not happy. Here it was snowing, move it on over, not snowing. That is how you get the contrapositive. Don't worry, we're going to deal with quite a few more of them when we practice, which is right now. This will be the first of a few slides in which you'll get the chance to practice all this symbolic logic stuff we've been talking about. Negation, conjunctions and disjunctions, contrapositives, the whole thing. | Understanding LSAT Logic_segment2.mp3 |
Don't worry, we're going to deal with quite a few more of them when we practice, which is right now. This will be the first of a few slides in which you'll get the chance to practice all this symbolic logic stuff we've been talking about. Negation, conjunctions and disjunctions, contrapositives, the whole thing. What the exercise is going to be is you'll go ahead and take a look at these statements. What I want you to do is I want you to write the symbolic form of the statement here, and then I want you to move from that symbolic form to the contrapositive, written also in symbolic form, and then I want you to say out loud to yourself the contrapositive in regular text. So take the statement, write it in symbolic form, write the contrapositive in symbolic form, say the contrapositive out loud. | Understanding LSAT Logic_segment2.mp3 |
What the exercise is going to be is you'll go ahead and take a look at these statements. What I want you to do is I want you to write the symbolic form of the statement here, and then I want you to move from that symbolic form to the contrapositive, written also in symbolic form, and then I want you to say out loud to yourself the contrapositive in regular text. So take the statement, write it in symbolic form, write the contrapositive in symbolic form, say the contrapositive out loud. I'll do the first one with you only because we didn't yet represent only if in symbolic form, and I want to show you how to do those necessary conditions because they're kind of interesting, kind of different, and after that I will set you on your way to do the other ones. So let's take a look at this first one. Daniel will come to the party only if Katie does. | Understanding LSAT Logic_segment2.mp3 |
I'll do the first one with you only because we didn't yet represent only if in symbolic form, and I want to show you how to do those necessary conditions because they're kind of interesting, kind of different, and after that I will set you on your way to do the other ones. So let's take a look at this first one. Daniel will come to the party only if Katie does. This is a necessary condition, a conditional that uses only if. What's the necessary condition? Well, the condition is that Katie has to go to this party or Daniel's not going to. | Understanding LSAT Logic_segment2.mp3 |
This is a necessary condition, a conditional that uses only if. What's the necessary condition? Well, the condition is that Katie has to go to this party or Daniel's not going to. It's necessary for Katie to come to the party, for Daniel to come also. So how am I going to represent this symbolically? Well, think about what we actually know here. | Understanding LSAT Logic_segment2.mp3 |
It's necessary for Katie to come to the party, for Daniel to come also. So how am I going to represent this symbolically? Well, think about what we actually know here. We can make a little if-then statement out of this only if. We know that if Daniel's at this party, what? Think about it. | Understanding LSAT Logic_segment2.mp3 |
We can make a little if-then statement out of this only if. We know that if Daniel's at this party, what? Think about it. Katie must also be at this party because she's a necessary condition for him being at this party. If Daniel's there, Katie's got to be there because that was a necessary thing. Daniel was never going to go unless Katie was there. | Understanding LSAT Logic_segment2.mp3 |
Katie must also be at this party because she's a necessary condition for him being at this party. If Daniel's there, Katie's got to be there because that was a necessary thing. Daniel was never going to go unless Katie was there. So as soon as we see Daniel, we know Katie is somewhere at that party also. Okay, let's move to the contrapositive. If we don't see Katie, this is negating the right side of the arrow, well, Daniel must not be there either. | Understanding LSAT Logic_segment2.mp3 |
So as soon as we see Daniel, we know Katie is somewhere at that party also. Okay, let's move to the contrapositive. If we don't see Katie, this is negating the right side of the arrow, well, Daniel must not be there either. This is negating the left side over there and bringing it over here. If Katie's not at this party, then Daniel is not at this party either. That's the contrapositive. | Understanding LSAT Logic_segment2.mp3 |
This is negating the left side over there and bringing it over here. If Katie's not at this party, then Daniel is not at this party either. That's the contrapositive. And again, I'll say it out loud so we have the full exercise. Here's the statement, Daniel will come to the party only if Katie does. It's represented as if D then K. The contrapositive is if not K then not D. And this statement, spoken aloud, is if Katie does not come to the party, then Daniel will not come to the party either. | Understanding LSAT Logic_segment2.mp3 |
And again, I'll say it out loud so we have the full exercise. Here's the statement, Daniel will come to the party only if Katie does. It's represented as if D then K. The contrapositive is if not K then not D. And this statement, spoken aloud, is if Katie does not come to the party, then Daniel will not come to the party either. Okay, now I'm going to set you on your way. Go ahead and pause your video. Again, don't do this out loud. | Understanding LSAT Logic_segment2.mp3 |
Okay, now I'm going to set you on your way. Go ahead and pause your video. Again, don't do this out loud. Do this on a piece of paper. It's much better for you to write down the symbolic forms to have that practice on the page. So grab a piece of paper, pen, pencil, and write out the symbolic form of the statement, the contrapositive, and then go ahead and say the contrapositive out loud. | Understanding LSAT Logic_segment2.mp3 |
Do this on a piece of paper. It's much better for you to write down the symbolic forms to have that practice on the page. So grab a piece of paper, pen, pencil, and write out the symbolic form of the statement, the contrapositive, and then go ahead and say the contrapositive out loud. And then I will be back to give you the answers in just a few moments. Alright, here we go. Every time a bell rings, an angel gets its wings. | Understanding LSAT Logic_segment2.mp3 |
And then I will be back to give you the answers in just a few moments. Alright, here we go. Every time a bell rings, an angel gets its wings. This is just an if-then statement. If a bell rings, then an angel gets its wings. So we represent that. | Understanding LSAT Logic_segment2.mp3 |
This is just an if-then statement. If a bell rings, then an angel gets its wings. So we represent that. B for bell. W for wings. Every time a bell rings, an angel gets its wings. | Understanding LSAT Logic_segment2.mp3 |
B for bell. W for wings. Every time a bell rings, an angel gets its wings. The contrapositive. If an angel is not getting its wings, well, there must have been no bell. And again, remember how I did that. | Understanding LSAT Logic_segment2.mp3 |
The contrapositive. If an angel is not getting its wings, well, there must have been no bell. And again, remember how I did that. I just took the right side of the arrow, negated it, brought it over to the left. Took the left side, negated it, brought it over to the right. If an animal is a mammal, it does not lay eggs. | Understanding LSAT Logic_segment2.mp3 |
I just took the right side of the arrow, negated it, brought it over to the left. Took the left side, negated it, brought it over to the right. If an animal is a mammal, it does not lay eggs. We have a little negation here, remember? Hope you caught that. So let's go with M for mammal. | Understanding LSAT Logic_segment2.mp3 |
We have a little negation here, remember? Hope you caught that. So let's go with M for mammal. If an animal is a mammal, then no eggs. Okay, now when we make the contrapositive here, remember the first step is to negate what's on the right side of the arrow. But there's already a negation here. | Understanding LSAT Logic_segment2.mp3 |
If an animal is a mammal, then no eggs. Okay, now when we make the contrapositive here, remember the first step is to negate what's on the right side of the arrow. But there's already a negation here. What are we going to do? Well, you know that just kind of like in math, two negatives make a positive. It's the same in logic. | Understanding LSAT Logic_segment2.mp3 |
What are we going to do? Well, you know that just kind of like in math, two negatives make a positive. It's the same in logic. If it does not not lay eggs, that's the same as laying eggs. So if it's not not, it's not the case that, it's not the case that the animal is laying eggs. That is the same thing as just a regular old E here. | Understanding LSAT Logic_segment2.mp3 |
If it does not not lay eggs, that's the same as laying eggs. So if it's not not, it's not the case that, it's not the case that the animal is laying eggs. That is the same thing as just a regular old E here. So we don't need to put the double negations. So when we negate this for the contrapositive, we're just saying that if an animal lays eggs, it must not be a mammal. That's the negation of this over here. | Understanding LSAT Logic_segment2.mp3 |
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